I suppose if you could find the motherboard and then buy a processor on NewEgg or something and rebuilt it... but then you'd have to get a copy of OS X intel legally somehow.. you could possibly make it fit. But, the price tag would end up being close to a new mini probably.. a 1.67GHz Core Solo is $250 on NewEgg I think, and not sure how much that motherboard would cost.
Not to mention the possibility of really really screwing up everything..
Oh and I do believe the new mini has a SATA connection for the HDD, so you'd have to find a SATA laptop HDD, and the new minis have different AE and BT antenas.
So I guess.. it's impossible. The Core processor WILL NOT fit into the old motherboard.
Edit: If you really wanna mod and it don't care about your warranty, overclock the old mini, put in a faster HDD.. things like that.