1996 Pontiac Trans Am Suddenly missing very badly & won

My beloved red 1996 TransAm, running strong as an ox Tuesday morning (and still looks almost brand new), wouldn't move Tuesday night. I've had it towed to TWO shops now and neither was able to diagnose it, let alone fix it. If anyone has any ideas, here are the symptoms: I can start it, but it misses very badly. Trying to move it, in 1st gear, it'll stall out or maybe move at 1 mph. Pressing the accelerator (even flooring it) does NOT affect engine speed at all.

Distributor and plugs have been replaced and spark at the plugs has been checked, fuel pressure is solid (so fuel pump is OK). Compression is solid, 150 lbs. There is NO 'check engine' light and so, all computerized diagnostics show that everything is good. Maybe it's the timing chain? The car has 278,000 miles on it and it's never been replaced.

Any help at all would be appreciated.