My 2010 Audi A4 58 won't start after giving a jump start, it was fine after I did then a few hours later my car stalled out and started throwing out all kinds of warning lights

does the battery still have power? if not when you jumped it with a low battery , You may have burned up the internal voltage regulator in the alternator. A low battery can do this.

I just put a new battery in the car, it's the 3rd battery this week, now it won't turn all the way over n Start , i checked the fuel pump fuse it's good I switched the relays and still nothing,I'm thinking possibly the fuel pump or the crank shaft sensor which I'm looking to replace tomorrow, that's just to get the car to start,now the message board was saying that I wasn't getting a charge from the alternator so I still have yet to figure that out due to the fact that I have to get the car up and running again to take and get a diagnostic test, I had codes come up last week mainly from the cooling system , p0299,p0420,p2181,p0562, nothing about the alternator or crankshaft sensor , ever since I got this car 6 months ago it has been nothing but a big problem which I have yet to discuss, just wanna get back on the road again before I get into the other issues please let me know what you think

sounds link the alternator was fried long ago when you first jump started it on the battery that went low prior to the three you purchased. The fuel pump is a Relay not a fuse it should click when you turn on the ignition, You could remove it turn on the ignition and plug it in and should hear the click as you plug it in. As far as a fuel pump problem that's possible but what I would do is have someone turn on the key while I was near the fuel tank to listen for the fuel pump to turn on for a second as it pressurizes the fuel system.You should only hear it for a second then it will turn off as the fuel system is pressurized. Next try to see if you have fuel pressure with the key turned. Watch this video and pay close attention to the fuel pressure sherader valve this is where you will check for fuel pressure. You do not need a pressure gauge attached to do this test just to see if there is fuel pressure. As you can see the valve looks like a tire valve and if you push in on the center of the valve fuel should come out ( keep a rag around it for fuel coming out. If the key is turned on then off the amount of fuel coming out will be minimal providing pressure was built up from the pump when the key was turned on. If the key is on when depressed the fuel coming out will be constant. I would try it with key turned off first should get a small amount of fuel as it bleeds down pressure. Now as all the pressure is gone turn the key on and off again to see if it has any pressure on the second try. If the fuel pump is working it will have pressure again. If the fuel pump is not working it will not have pressure again . Next if no pressure and you don't hear the fuel pump coming on You can try some starter fluid sprayed in the throttle body as you try to start the car. If its a fuel problem and not a Crank or cam sensor it will start and run as you spray starter fluid.

this is the video ......https://www.bing.com/videos/search?q=2010+Audi+A4+58+fuel+pressure+test&&view=detail&mid=463F5324D24B89AAFBF1463F5324D24B89AAFBF1&&FORM=VDRVRV

Remove the alternator and battery and take them to the parts store to be tested and charge the battery .Both must be good. While at the parts store get the starter fluid and a fuel pressure gauge. You might be able to rent.When you rent a tool you are paying for its cost but when you return it there is no charge at all ( it's free) .You wont know if it is the cam or crank sensor till you see if its a fuel problem with the pressure gauge and starter fluid.