the part you need to replace is the hinge "clutch" - it should be possible to do, if you're comfortable disassembling your machine. There are 2 clutches, left and right.
I've successfully replaced the hinge clutch on my previous laptop, a PowerBook G3 "Pismo". it required pretty well taking the whole unit apart - however repairing the hinges does not require you to replace the whole display. After taking apart the machine, it was clear which clutch was broken (in my case, only 1 was broken and needed replacing)
I bought the replacement clutch parts from another site several years ago (before I came across ifixit.com!) - but I notice you can buy these kind of parts here on ifixit too
I don't know the detailed inner construction of the Aluminum PB G4, but I think it's similar, as far as the display hinge goes.
the actual replacement of the hinge parts is easy - it's the disassembling the rest of the machine to get at them that's all the work.