not the easiest thing in the world to do, but if you have the ntuser.dat from the old machine you should be able to extract it..
I suppose the easier thing might just be to ask why you can boot the old install and work from there.. but if you remain committed to pulling it from the old install without repairing it:
1) Find the ntuser.dat file from the old machine (c:\documents and settings\<username>). If you don't know which ntuser.dat file contains the key, try them all..
2) Grab a copy of LoadHive and run it and use it to select the ntuser.dat file (leave Loadhive running)
3) start regedit.. browse to HKLM and look for a new subkey called NTUser.. HKLM\NTUser\Software\Microsoft\Windows NT\Current Version. (note: it may also be under HKLM\Software_00\Microsoft\Windows NT\Current Version)
4) Open the DigitalProductID key
5) Grab the information in bytes 52 through 66 (see example - you want the info marked with "1's" - also in bold and underlined.. note: your data will not be 1's but should be a series of hex data.
0000 00 00 00 00 00 00 00 00 ..
0008 00 00 00 00 00 00 00 00 ..
0010 00 00 00 00 00 00 00 00 ..
0018 00 00 00 00 00 00 00 00 ..
0020 00 00 00 00 00 00 00 00 ..
0028 00 00 00 00 00 00 00 00 ..
0030 00 00 00 00 11 11 11 11 ..
0038 11 11 11 11 11 11 11 11 ..
0040 11 11 11 00 00 00 00 00 ..
0048 00 00 00 00 00 00 00 00 ..
0050 00 00 00 00 00 00 00 00 ..
6) Use the utility attached, input the hex code to decode the key.
Alternative:
Export the value that contains the DigitalProductID value to a file, edit that file to keep only the DigitalProductID value.. modify to import back to HKLM\Software\microsoft\Windows NT\Current Version
Export your current HKLM\Software\Microsoft\Windows NT\CurrentVersion key
Merge the reg from the old computer into HKLM\Software\Microsoft\Windows NT\CurrentVersion key
Use the magic JellyBean to pull the key
Reimport the original Reg key to restore the correct key
I would still recommend using a test machine or use VMware/VirtualPC to setup a temporary computer and not your primary machine as it will change the key.