When you say jump started, I assume you're meaning using jump leads and a second battery. If that's the case, I would get a second opinion on the battery. How was it tested? Also whilst car is running, test the output from the alternator with a multimeter. Should be between about 13V to 14V with everything turned on, lights, aircon, heated windows, the lot. If it less than 12.5, suspect alternator, if its more than 14.5V again alternator.
Other than that, next port of call would be a lazy starter or sticking solenoid.
After that you're into some kind of intermitent electrical fault .
Aim low, play Bass!