I have a brand new battery and a brand new alternator in my 1989 Toyota Camry. i recently got a tune up, new breaks, and also an oil change, BUT for some reason my car randomly doesn't want to start, but once i jump it, it instantly starts back up. Within the next week or two it does it again. I've been told by numerous people that it's not my battery, and may have something to do with a relay.

Find it near the oil filter

sparkplugs, air filter change and oil change.

pretty simple, took me about an hour to do everything.

It is strange ! But anyway, check the wiring from battery to alternator and the earthing wiring. Have you used a new alternator or not . If the alternator is a second hand one have you checked it if is working before fitted on the car ?

I suggest to check if you have oil leaking onto your alternator or did you recently replace the alternator? Keep in mind that the voltage regulator is built into the alternator on vehicles and I have seen oil leaks internally short the alternator or poor quality aftermarket parts.

Also check ground and wires broke or in short.

replace temputer sensor to fix cold start problem . check for bad alternator and fuses for battery

It could be your starter going bad. The added boost from the jumpstart may give it enough cranking amps to overcome the starter failure for a short time.

Seems like this car have the same symptom wherever it is, I have this trouble as well, I did the tune up, injection cleaning, change spark plugs and spark plugs wires, change the air filter, change the engine mounting but still the same trouble :(

Have you try putting some Fuel System Cleaner addictive? If you have, then you haven't really try the only one that works -- Lucas Oil brand "Upper Cylinder & Fuel Injector Cleaner"

It is the best one and only one that works effectively. 3oz. will treat a 10 gallon gas tank. A small bottle cost $6 or you better buy a big 32oz. bottle for $12. Keep it and do it every other oil change.

If I were you, I will put it into two tank of gas back-to-back so your car's fuel system can get a good cleanup over a couple hundred of miles.

Similar problem for my 89 camry. It ended up being my in tank fuel pump that had died.

check alternator wires and replace regulator