To clear up a misconception, the generator won't drain the battery. If two of the six diodes are shorted, it will draw REAL high current and blow a large fuse or melt a fuse link wire. What it will do is fail to recharge the battery while you're driving. That's a technicality but the result is the same. You're running on just the battery to keep the engine going, and that won't last very long. Even if you use a home battery charger to charge the battery for a couple of hours, it will only run the electric fuel pump and the many computers for perhaps an hour; less if you run the heater fan and head lights. If you start with just a jump-start, you already have a run down battery so you'd be lucky to keep the engine running more than a few minutes.
Use an inexpensive digital voltmeter to measure the battery voltage with the engine running. It must be between 13.75 and 14.75 volts. If it is low, suspect the generator, but there are some voltage checks that should be done on it first to eliminate any possible wiring problems.