Saturn ion 2 will not start

I left for out of town for 3 days and when I came back to start it, it was completely dead. Battery dead, wasn't making any kind of noise. I had it jumped and it started but then it started shaking really bad, I would rev the engine and after about 300rpms it would stop shaking but as soon as I would release the gas and it would go back to idle, it would Shake again... When we went to try to drive it, it wouldn't go more than 25 mph. I had it towed back to my house and now trying to figure out what the problem is. I checked the battery and it is reading full but now when I try to start it, it is just clicking and won't turn over. Any ideas?

need a load tester to see if the battery is good. voltmeter only checks the voltage in it, not the amps. most auto parts stores with test it for you for free