MS Windows 7 computer locking up several times during the day

a bit too vague to suggest too much.  is there a point in time that this started? when you say lock up, are you talking about unresponsive everything, screen frozen, mouse note moving? do you ever get blue screens?
does control alt delete do anything?

if a point in time can be identified when this started then try uninstalling software installed since then or even better perform a system restore to prior to that date.

First, backup all of your important data to another location...external drive, thumb drive, etc.

Then look through Programs and see if anything is installed that shouldn't be.  If you find anything remove it.

After that run a full anti-virus scan and malware scan.

If the problem doesn't go away I'd wipe the drive and do a re-install.

I've tried to fix issues like this before and spent days trying to figure it out and I always wound up doing the backup, wipe, reinstall, and restore data.

you can also try disabling startup items and services that you may not need using msconfig (windows_key+r, type msconfig and press enter) and see if that gets you anywhere

a lot of times complete lockups are caused by device drivers.  have you installed or made any changes to the hardware.  have you installed optional windows updates such as updated device drivers lately?  see if you can correlate a change to about the time when lock ups started

This PC is only 3 months old.  I've run virus checks yesterday and it did find a Trojan that was removed and cleaned (including hidden files) on the Admin side.  The locking up is unpredictable - she is working and everything just feezes and we have to reboot to get it to work.  It has progressed since 08/23 from once a day,m to 5 to 6 times a day.

Could be a few things:

1) Software: open up the run command and type msconfig, choose startup tab, remove unneeded programs from auto-starting.

2) Hardware:  Run memtest to see if maybe you have a bad ram module (http://www.memtest86.com/)

Also could be a defective hard drive (you can download the manufacturers HD diagnostics tools or depending on your PC you can run a diagnostics scan on startup).

Open up the system and see if there are any blown/leaking capacitors, (look at all the cylidiner shaped objects on the motherboard, should have flat tops).  A defective one will usually show a buldge on the top.

I have also come across this issue with a bad power supply (even when the power supply tested good).

Even though the system is relatively new it could still have a defective module (hate it when that happens).

We changed out our servers, and had to repoint this computer.  It was then updated from Office 2003 to Office 2010

Especially when lockups occur randomly this points to a hardware failure. My advise is to check your harddrive with GRC's Spinrite:

https://www.grc.com/sr/spinrite.htm

Has saved my bacon a couple of times. Not free, but just works. Comes with 30-day money back guarantee, no questions asked.

since your system is relaticvely new, i would ask for a warranty replacement, since you said " It has progressed since 08/23 from once a day,m to 5 to 6 times a day. "
so it started from the install date

I've requested that this question be deleted for the following reason:

Not enough information to confirm an answer.

This turned out to be a faulty Mouse

This was caused by a bad mouse