Is it possible to install a hard drive from a new computer into an older computer you tried it and your computer freezes up at the starting windows screen

Make sure you are installing the older hard drive as a second drive, not the initial drive used for boot-up.

Be aware that some Microsoft products have a dumb copy protection system that prevents you replacing faulty drives. You have to phone them for a new licence key if you alter hardware components.

You may need to move a jumper to make the drive a "slave" not a "master" drive.

Your computer will boot-up using its normal drive. It should boot up fine. If you can see the second drive you can then copy files off it.

If you cannot see it, you may need to get into the BIOS setup and changes setting there. That's an advanced topic, not easily written about here.