A few thoughts...
During 25+ years in the industry - I've seen drives that could ONLY work as a slave - didn't even try to figure out why once that was established..but would assume something wrong with a portion of the drive hardware that was ONLY used when the drive was configured as the master...
Beginning with XP - "Microsloth" started experimenting with a lockdown match to the hardware the OS was installed onto - a very sloppy overkill method to use the computer hardware to stop piracy of their precious OS - you might try wiping the drive clean and seeing if the new machine could recognize the drive once the original install of XP was removed from the drive..??
Also a possibility that it could be an incompatibility between the BIOS level of the new machine and backwards compatibility to SATA 1 hard disks - or the firmware of the hard drive itself not being compatible with the newer motherboard/controller/machine - although any manufacturer should be shot for not allowing backwards compatibility for at LEAST the last couple of generations of hardware...Perhaps a BIOS upgrade might aid in getting the new hardware to recognize the older drive..?? Or a firmware upgrade to the drive itself might allow the newer hardware to recognize the older drive...Again, makes NO SENSE - but a quarter century of hardware engineer experience has proven that not all vendors remember to consider older hardware when designing their "latest and greatest"... And it certainly would not be unheard of to need to upgrade the firmware on older hardware to allow compatibility with a newer generation of hardware...
Guessing about jumper configurations is a needle in a haystack approach that is only successful if one gets extremely lucky - the earlier post about doing a Google (or whatever)search for the specific manufacturer/model numbers of the hard drive AND motherboard in question should provide you with links to the manufacturers websites - or other sources - that would provide the tech specs and manuals for both - and perhaps your answer would most likely lie in the documentation found by such a step.
Let me know if these tips are of no help...and I'll try to help you find an answer beyond those "expert" tips provided by the other old fart posting here - who apparently is interested in nothing beyond attempting to aggravate you and your quest for a resolution...
And, unfortunately - it IS always possible that there simply IS no answer...the drive could have been zapped in the move somehow.. any number of possibilities there... :-(
Feel free to contact me at ron_ruble@yahoo.com - be sure to include reference to this thread and your specific problem in the subject line - as my offers to others such as this have obviously earned me large amounts of spam/junk/useless mails to my address from others like Mycroft who don't appreciate others speaking the truth about their helpful posts...and delight in seeing that I'm added to every spam list they can find... ;-)
Best of luck in your quest...
Ron