Do you want to use the standard speakers? Cos other wise you really don't need to bother finding the old loom! All you will need to find is accessories power, get your multimeter and find a wire that has power when acc is on and nothing when its off easiest would be cigarette lighter i think. And constant 12V, a wire straight from the battery with a fuse in it is what i usually do because i find that easier than crawling around under the dash trying to find lve wires. You put in your own negative cos its really easy and i suppose you would have to find the aerial lead though that shouldn't be hard!
So yeah just run your own speaker wires because then you don't have to find the old ones, the sound wil be better and a lot of older corollas use a common negative that is meant to blow the amps in new head units.