Windows 7 computer hangs at welcome screen.

Well, I think the first thing is to do some diagnostics on the hard disk or SSD that windows is installed on.
You can get a nice Windows PE boot disk/USB stick by downloading Hirens WinPE Here
Or if the computer is like a Dell, or an HP, it may have hardware diagnostics built into the system, and accessed by pressing a special key at startup like F12 for Dell, or Escape for HP, etc.
If the disk doesn't have any physical bad sectors, then we need to attempt to repair the problems with the Windows install that are preventing it to boot correctly.
First of all, if you are getting to the Windows Logon or Welcome Screen then there is most likely nothing wrong with your boot files, and BCD.
By pressing F8 at startup you can enter the "Repair My Computer' link, and start the Recovery Console (RC).
Here are many tools to repair Windows 7.
Start by opening the Command Prompt (CMD).  and running:

chkdsk c: /f

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.
This will scan for and attempt to fix disk and file system errors.
if this finds errors and says it repaired them then try again.
If not booting still then go back to the RC, and open CMD and run:

sfc /scannow /offbootdir=c:\ /offwindir=c:\windows

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Replace C: with the current drive letter for you Windows drive, if its different.
When complete try again.
If not booting still, then try booting back to the RC and using System Restore to go back to a previously working registry and system files.
If none of this is effective, then without a valid disk image backup, from Windows Backup or other program, done before the failure, you may be faced with backing up and reloading the computer.
If this happens, one can use Transwiz  to make a backup of the whole user profile, including files and settings, save it to a .zip file and then when the computer is rebuilt, can use to restore profile to new load of Windows.
Let us know how you do...

plse post the disk model - then we can advise you what diagnostic tool to run
your disk may have bad sectors, or can be dying
for an SSD, i suggest you run the SSD toolkit from the manufacturer, for HDD i use the diag tool  from the manufacturer
you find all you need on the UBCD

Hardware diagnostic CD    UBCD
---------------------------------------------------
go to the download page, scroll down to the mirror section, and  click on a mirror to start the download
Download the UBCD and make the cd   <<==on a WORKING PC, and boot the problem PC from it
Here 2 links, one to the general site, and a direct link to the download

since the downloaded file is an ISO file, eg ubcd527.iso - so you need to use an ISO burning tool
if you don't have that software, install cdburnerXP : http://cdburnerxp.se/

If you want also the Ram tested - run memtest86+ at least 1 full pass,  - you should have NO errors!
direct download :  http://www.memtest.org/
 
For disk Diagnostics run the disk diag for your disk brand (eg seagate diag for seagate drive)  from the HDD section -  long or advanced diag !  (runs at least for30 minutes)

http://www.ultimatebootcd.com/      

**  you can make a bootable cd - or bootable usb stick
*** note *** for SSD drives  use the tool from the manufacturer, like intel 's toolbox :
https://downloadcenter.intel.com/download/18455/Intel-Solid-State-Drive-Toolbox

for completeness -here's how i handle disk problems : http://www.experts-exchange.com/Storage/Hard_Drives/A_3000-The-bad-hard-disk-problem.html

==>>****in order to be able to  boot from CD or usb - you may have to disable secure boot in the bios

you may think of converting the disk from mbr to gpt prior to use the repair tools. you would need a windows 10 computer and the system tool mbr2gpt.exe which is part of windows 10 since version 1803. take the win7 disk from computer and put it into an usb 3.0 adapter. those adapters are not expensive and you will easily get them for m.2 ssd, normal ssd, and 3.5 sata disks. connect the usb adapter to win 10, and add a drive letter for it (by disk management) if not be done automatically. then, you best would clone the disk to a 3rd disk or NAS. if successful use the mbr2gpt.exe to convert the disk. on success try if the conversion did repair the issues. if not, reboot the win 7 to the command prompt then type
   

c:\windows\system32\diskpart> diskpart

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        diskpart> list disk

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if 0 ist he correct disk number

        diskpart> sel disk 0

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        diskpart> list vol

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the EFI partition is formatted with FAT32. assume volume number is 3 and letter K is not used

        diskpart> sel vol 3
        diskpart> assign letter=K
        diskpart> exit

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c:\windows\system32> cd /d K:\efi\microsoft\boot\
K:\efi\microsoft\boot> ren BCD BCD.old
K:\efi\microsoft\boot> bcdboot c:\Windows /l en-us /s : All

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if this still doesn't work, you could try to only have the GPT partition with the windows c partition. the remove all other disk and delete all boot partitions in bios beside of the one disk.

if there is only one choice uefi is able to say windows to start without efi partition.

Sara