1999 S-10 sometimes dies after start, when you give it gas

Hey, I'd really love some help with this one, mechanics keep 'fixing' it, it happens again.

1999 Chevy S10 pickup, automatic, just hit 90,000 miles. Replaced alternator 2 years ago.

Simple version:
The car runs fine in neutral no matter how much gas you give it, and seems fine in gear until you really step on the gas, and then it dies. Sometimes it acts like the battery is almost dead. This only happens once in a while and seems fine after a visit to the mechanic.

Full version:
This has happened three times over a year, all slightly different. My memories about the battery might not be right.

1 year ago, it wouldn't start, battery seemed dead, got a jump and the car started and idled fine for a while, drove a few feet and then died. Shop told me the computer was cutting the engine due to a fuel pressure problem. Cleaned fuel system & changed fuel filter, didn't have the problem again.

A few months ago, it wouldn't start, battery seemed low. Got a jump and the car started and idled fine for a while, drove a few feet and then died. Shop said they couldn't find anything wrong but bad battery contacts, said my battery was due for replacement anyway & put a new one in. Didn't have the problem again.

Last night it started up on its own but was acting strange, drove a few inches and then died. Wouldn't start again. Got a jump, made it home ok. This morning, started up on its own, backed out of the driveway, put it in drive and hit the gas, it died. Currently starts and idles fine, haven't tried to drive it anywhere, but doesn't seem to be stalling right now. In neutral, sounds normal, with a slight vibration when I give it a lot of gas.

Was it an intermittent spark plug problem or a broken steering column wire all along, with shops fixing other things? Or? Don't know what to tell them to look for when I take it in this time. Worried it will happen on the Atlanta highway.

Other related (?) Issues: headlamp light sensor doesn't work, headlamps are on all the time, headlamp fuse gets hot. Very easy to 'miss' ignition position with the key (turn past it). When the key is removed, the temp, oil, fuel guages seem to come back on after about 20 seconds (the needles pop back up, but not all the way to the reading they give when turned on normally).

Thanks for any help you can give me!