There is a good chance you would get a BSOD when trying to boot a hard drive with Windows on a computer with different hardware. I am surprised the Alienware 51 had a motherboard that old. The computer is like the one in my Alienware 51 link? If so then somebody switched out motherboards if yours is indeed a D935xebc2
I would do the following. Clean off the CPU and heatsink and apply thermal paste. Attach the hard drive back into the computer. Download a linux iso like Ubuntu or Mint. Start with 32bit. How much RAM is on the computer? Anything over 1 GB should run linux fine.
I am pretty sure Windows 7 is too much for a Pentium 4. Go with XP if you want a Windows OS but as you know security updates are no longer available for XP. Ubuntu may even be too much.
Edit: Here the SL724 page. According to Wiki and intel the processor is 32bit. You may be able to run Windows 7 32bit. Mint and Ubuntu would run well if there is over 1GB of RAM.
Edited by JohnC_21, 26 March 2016 - 03:08 PM.