The fact that you drove it for 30 minutes and failed to charge the battery to a sufficient level leads me to believe that the alternator has no output, or the battery is in such poor condition that it won't accept a charge.

The former can easily be checked with a voltmeter. Bring the engine up to 2000 rpm and the reading must be 13.5 volts or more.

The latter can be checked by any decent seller of batteries using a load test.