Getting files from old hard drive

I have a Lenovo G580 with windows 8.1 on it. The computer failed to boot up yesterday and it said something like boot failure. I guess the PC is not reading the hard drive. I took the hard drive out and installed it into my old Fujitsu A3210 and Fujitsu is windows vista. Anyway I was able to put the hard drive in the Fujitsu and when I turn it on I can go to BIOS and stuff. So what is my next step here? How can I be able to get to the desktop to see my files? I did the diagnostic thing and it ran and rebooted and it says "initial diagnostic test completed successfully. Bios continues full diagnostic test. Hit any key to continue." Once I hit any key it brings me to a black page with nothing on it. So should I go into BIOS to change boot order or something or how can I get to the log in screen to access my desktop?

First, you have created all sorts of trouble for yourself by swapping in a different hard disk with a different OS into another computer and expecting it to run. Probably more trouble than that is worth.
HARDWARE IS DIFFERENT BETWEEN THOSE COMPUTERS! The drivers are different. The equipment won't know what to do with the drivers on the hard disk, and can't run without proper drivers it had before.
Better is this--buy a hard disk enclosure for USB external drive and put the Lenovo disk in it. Connect to the Fujitsu computer. Run the Vista and look for a new hard drive letter. That is your Lenovo disk. Get files off it.
But I don't think all of the above is even necessary. The Lenovo has nothing wrong with it besides a failure to boot up once. You can cure it with its own hard disk. Try these--
Put disk in it, turn on and go to Safe Mode. Try Startup Repair. This is a good tool available in Win8 and 8.1.
If no luck there, then run system file checker (sfc.com /scannow in a command or "RUN" window. Only Windows files will be repaired.
If you have no luck, then make a bootable USB or DVD that has the Windows 8.1 on it. There are free downloads to do that. You can then do a Repair Install, not a full install. Your Windows files will be changed, but no other ones. Might have to do updates after that.