2003 Alero (3.4) wont start or even attempt to turn over until jumped. While driving I can hear whining through the speakers (with radio off) that matches the engine RPMs. Once I turn the car off, it loses all power, no gauge lights, radio or anything and wont start until I jump it. I also noticed that when in park if I quickly punch the gas I lose RPMs before the engine revs up...sometimes the car will stall and then restart itself on it's own...other times it will die and all my dash lights will cycle and the tach/speedo will cycle and then the car will be completely dead again until a boost. Sometimes if I have the ignition at the first notch (not accessory, run, or start) I will see a faint check engine light and if I hit my brakes the dash lights will power on and the tach/speedo cycle then go out and the car is dead again...It's not the alternator (took it out and had it tested and it's fine...the car ran fine for over an hour once started today).

Wow, that is quite the electrical psychoanalysis :0) You have got some major electrical issues going on here. Well, the first things that I would suspect to even get a little idea as to what is going on, considering that you have multiple systems with electrical failure and some are not even related systems that should be in any way connected, I would check first the main computer. It sounds as if the main computer system could be on it's way out to complete failure. However, I am not even sure that the computer could cause so many system wide failures, therefore, I would also be very suspicious of your main wiring harness. Years ago, I had an old 1968 Datsun Roadster Convertible. They used to call them the Datson 311, it was the pre Z care before building the first 240Z. I had multiple systems intermittently failing and coming on at all times, hit the horn and the lights go out, press break and lose power to the stereo, etc. I did not have quite as crazy of a system problem that you have, but it was pretty bad when my lights went out driving over the mountain pass in the middle of the night when I hit a bump at 65mph. What I discovered is that I had an overheat problem (never did find the cause) that melted my main wiring harness together at the block where the harness enters from the engine compartment through the firewall. As a result, wires became cross wired and shorted out intermittently because all the coating had melted of the wires and every-time the car bumped even just a little, systems would change and wire into other systems. Not a very common problem, in fact very very rare, but you have very uncommon symptoms so who knows, maybe I have seen it happen twice in a lifetime.
Good luck, and if you figure it out, post your solution. This is one I would love to know the answer on since it is so unique.
Good luck
SCSTOCKS

Look for the troubles in the user manual of your vehicle. I am sure you will get the best solutions relating the troubles you have been facing in your vehicle.
And if you do not possess the user manual, you can get a copy of it online, Visit manuals.co, which is the online hub to get all kinds of user manuals for vehicles absolutely free.
Free Car Repair Manuals Online Workshop Documents in PDF