If you have a voltmeter, you can pinpoint the problem. Put the leads of the meter directly on the battery posts ( not the clamps ). Try starting the car. Normally, the voltage will drop to about 10 volts because of the load. If it drops much more than that, the battery is bad.
If the battery appears OK, move the leads one at a time to the clamps, the engine block, etc. until you get a big drop in voltage when starting.
I assume that when jump-starting the car, you connect the negative jumper cable to the engine block (proper procedure). Doing this bypasses the existing negative battery cable which is probably your problem.