Do you think my Dell Inspiron should be retired?

Yes.  It's been 7 years.  Time to get a new system.

I think that is a consumer model so 7 years is good life. Get a bootable DVD or USB key and recover the data to a USB hard drive and then replace it

That it booted the USB drive suggests there is nothing wrong with the hardware.

Seven years is a reasonable lifetime for a desktop.  However, if you find the system's performance still acceptable then it's certainly worth looking into what the problem might be.

Normally I would say "First go into the event logs and see if the system was logging repeated errors of the same type before the failure."  However, if Windows will not boot even to maintenance mode then this is not an option.

Take a good bright light and carefully inspect all the electrolytic capacitors on the motherboard, and the region around them.  The caps should not be bulging, deformed, have split tops, or be exuding gunk onto the motherboard.  If the motherboard has   a four-pin power connector next to the CPU, particularly examine this for burn marks both on the nylon shroud and on the board.

If the caps are intact then run Memtest-86+ on the system for at least 24 hours.  If it passes that, then the system shows promise of being rebuildable.  Get a utility CD/DVD with the disk manufacturer's drive utilities on it, check the SMART status on the drives, and if they show no problems then run the driver manufacturer's diagnostic(s) at the most aggressive level.  Then if the system passes that, run the built-in Dell diagnostics (if they're still runnable).  If that passes, then erase the drives using a utility such as Darik's Boot and Nuke, install a fresh copy of Windows and run it for a few days to see if the problem is resolved.

Systems do become old and crotchety and sometimes beating up the hardware a bit and a fresh reinstall solves the issue.  Anyone who has been in this business for a while either believes in bit rot, or should believe in it.

Also remember that BIOS needs to be updated (new requirement since 1/1/2018 over a year ago) and then 7 years predates Windows 10 by several years in terms of effective design.

I would replace it if it were me.

Calculate the cost per year.

Generally, I've found that an "upgrade" (e.g. SSD, RAM) of an existing system at around year 2 or 3 to be the best deal.  Beyond that, I've found that purchasing a new system is more cost effective.

You're at year 7.  In these cases, it's only "worthwhile" to put in a new disk or add RAM if you happen to have those extras as spares from upgrades of other systems as they trickle down.  Buying a new disk or SSD to "repair" this ends up costing more per year in terms of investment.  It's old tech.  Time to cut your losses and maybe donate it to a non-profit that will refurbish it for needy schools.  How many more years do you plan or expect to keep it?

Replace it, unless you have existing spare disks.

Update:  very helpful comments - thanks..

Here’s what i have done/plan to do:

1) i have a recovery image saved (i forgot i did one last month prior to traveling a ton - which causes memory loss from long plane flights).  
-currently, i’m Running the system restore via my disk image on a separate USB drive.  (I booted to a usb boot disk in order to accomplish this
2) i’ll Let it run and see its course.  I appreciate the comments about diagnostics. The image restore process will dictate just how far i go on diagnostics..

3) since i was out for a meeting, i  bought another Dell at costco.  I3670.  The deal was $700 with core i5-8400 12G Ram and 1 TB.  Included a monitor which i don’t need: see below

I went with a majority survey above and agree that it’s prob time to retire the old one, but not before letting it run some diagnostic repair in parallel to see what can be done ( yes donate it etc.  good cause as it could still be a great machine and with a 27” dell monitor - it could potentially set someone up..

Will post when done the image restore function..

Any chance of sending the 27 inch monitor my way? Only got an i3 based laptop at the moment, good enough for streaming video and watching porn but not powerful enough to win at any online games,

I just finished a restore from image disk process - it went fully complete, asked to restart the computer, then went through the Dell icon, then to a command line message that reads “Missing Operating System”.

I will look around but this sounds fatal to me at the board level.. ?
Thanks

Could be the motherboard or corrupted operating system. See if you can boot with a bootable USB Key completely bypassing the operating system. Does this work?

I would be inclined to suspect that there's a problem in the restore software.  Try installing Wndows from standard distribution media.

I’m retrying with the bootable USB that i created from same PC.  This time, same “missing operating system” message comes up even though i’ve Changed the boot sequence to USB where the recovery USB is located..

Hmmmm

Third try on boot through USB drive works to Advanced Options screen.  Select ‘Start up Repair’ and received same error that message that Win10 start up repair “couldn’t repair’ my PC..

You need to try a bootable operating system. Try a Knoppix bootable DVD.  It does not matter what OS, just that it is not trying to use the operating system on the computer.

That usually indicates an error on the disk.  The OS is on the disk.  It's not finding the boot disk.  Are the 2 disks in RAID, or are they set up as 2 separate disks.  Maybe the boot sector is corrupt.  See if you can fix that.
https://neosmart.net/wiki/fix-mbr/

Cost of a new hard disk for Dell Inspiron? About $15.

i would Always run ram and disk tests when i meet such problems - to be sure about the basics
i use the ubcd  for this :
https://www.experts-exchange.com/Hardware/Components/Motherboards/A_1945.html                  (Short-overview-of-how-to-troubleshoot-bad-hardware-when-a-pc-does-not-post)

this vcan help too : https://www.experts-exchange.com/Storage/Hard_Drives/A_3000-The-bad-hard-disk-problem.html

and imo, the system still is worth repairing.
if the disk is bad, i suggest to replace it with an SSD drive  -   here a 1 tb one  https://www.amazon.com/Kingston-960GB-Solid-SA400S37-960G/dp/B079XC5PVV

thanks all.. if there is a way to split the credit, pls let me know.  it appears to me i have bad sectors (without going deeply into the diagnostics).  my plan is to harvest the data (where possible) from my disks and let the old box ride into the sunset..

On a lark, i removed both HDD’s and placed them in cases where i attempted to read each from the new PC.  As it turns out, the SLAVE HDD didn’t read and indicated corrupted sectors.  I could have run some clean up apps, but since it only had data (backed up), i proceeded to format it.  

I checked the Master HDD and it read fine on the new PC.  I reinstalled the Master back to the Inspiron 660 and it ran fine.  

It appears that the Slave HDD having corrupted sectors caused the Boot process to hang.  

In the process of cleaning up the old Inspiron.. i’m fully baked on the new Inspiron 3670 so no turning back but will donate or find another use for the old one.  My gut tells me that it will soon follow suit as the Slave HDD.

I’m fully baked on the new Inspiron 3670  

So you retired the old machine, have a new machine, and now if you need data from the old drive and it will spin up, try Recuva or GetDataBack  (https://www.runtime.org/data-recovery-software.htm)