Friend of mine just bought a pretty cherry 87 Supra Turbo with a 5spd, but the turbo apparently doesnt work. He wants an OE turbo, not an aftermarket. If anyone can direct me to a starting point I`d appreciate it.

Also, any inherent issues/problems that are usually found on these cars? I know they are fairly complicated and lots of underhood shit is computer controlled, so they sound like a handful when they get some miles.

if your looking for original equipment turbo then the only thing i can suggest since you don't want anything aftermarket is to directly to toyota for it. and as for problems, they have a problem with blowing headgaskets due to under torqueing of head bolts from factory. Installing a metal headgasket, of course after you make sure the head isn't warped and check the mating surface of the block, will pretty much solve your problems. But no need to go ahead and change it until it blows, unless you rather just do it as a precaution.

you could pull the turbo off and have it rebuilt or even upgraded
have a blast go fast !
http://www.ddmcse.com/turbo/turbo_upgrade.htm