Computer bad?..............

My 1989 3.9 4WD battery charges just fine when it is sitting in the driveway, but if I drive it 20 miles to work, the battery is dead when I get there. So I leave it running for 20 minutes so it will start when I go home. Anyone ever heard of this before?
Brand new battery, new alternator.
It is strange that it seems to only charge when it is out of gear. One thing I noticed is that the 4WD light stays on even when it is not in 4WD. Could there be a short there, that is causing it to lose the charge when driving? I seem to think it is the computer, because I found out that this was the first year the voltage regulator was in the computer.
HELP - any ideas would be greatly appreciated.

what does the voltmeter in dash show when your driving and if you dont have one you could pick up a cheap digital volt ohm meter and probe the + lead to your cigar lighter or an empty fuse terminal that has voltage and ground other lead and then monitor your charging while driving should be 13.1/2 -15 volts depending on the state of the battery

your pulley on your alternator may be the wrong size. If the pulley is to small then the alternator spins to fast and the voltage regulator does not let power goto the battery for charging. Also just because the alternator is new does not mean it works.