alternator. 1990 Camry's alternater is very easy to be replaced because there is lot of rooms under ther hood.
You need to buy a Haynes repair manual which is better than Hilton's. I could not find it in Amazon. Try to get one from a local parts store.
With a repair manual, you could do almost everything.
You have to have a ramp, jack, jack stand, wheel choke. Be careful working under the car. Safety is the first thing you have to pay attention to.
Your car, I think the starter is broken since jump start from another car would not jump it up and also there is no cranking sound.
But is is highly unlikely that both starter and alternater die at the same time. I think, if I were you, I would start to replace starter first. Some starter has built-in solenoid switch. Some start has no built-in solenoid switch. If solenoid switch is a separate part, this could be the problem rather than the starter itself.
You could try this first: locate your starter, use a hammer or something like rubber headed hammer (but don't do it too heavily) knoking on the start's solenoid switch while some one is cranking your car. Sometimes, the metal bar which is acting as a contacting point for the switch in the solenoid switch stocked and could not be down to the circuit points so you would not be able to crank the engine. Be careful if working under the hood and car is starting, be away from the moving parts. Put the brake on, with another person as an assitant.
I get rid of one line originally in this line. It is dangerous to try.
If it is not working by this trial, your starter or starter's solenoid switch is broken.
You could buy a code reader, under $20 on ebay or amazon. To check the code, you might find where he problem is.
Good luck.