Drove 1996 3.1L Buick Century to Pennsylvania from TN. While there, developed issue of not going into first when pulled to D. Would not engage, until I put it into 1. From Stopped position, I could rev engine, but get no engage of 1st. I'd let it settle, then put into 1. This would engage and allow me to shift normally. This lasted for a few days and still happens intermittently, with no pattern, still. Also will hold onto first to very high rpm, then shift out of 1st, past 2nd, directly to 3rd. This, also has subsided since return trip from PA to TN. I've also noticed that taking foot off brake and pressing accelerator, there's a lag until 1st engages, then engages hard, but now shifts normally unlike during trip to PA, running through gears 1 - 3 or Overdrive.

Is this a sticking solenoid? Fluid level is slightly 'above' cross-hatch area on dipstick; no frothing of fluid noted. Using high-mileage fluid.

Does Throttle Position Sensor play into this?

You might look at BNaylor's thread at http://www.automotiveforums.com/vbulletin/showthread.php?t=899929
He describes more hard upshift problem, but often the 4T65E tranny will also show symptoms like yours in addition to hard shifts. My wife's didn't engage right away and had the hard upshifts, and BNaylor's fix cured both. Hope this helps you!

You might look at BNaylor's thread at http://www.automotiveforums.com/vbulletin/showthread.php?t=899929
He describes more hard upshift problem, but often the 4T65E tranny will also show symptoms like yours in addition to hard shifts. My wife's didn't engage right away and had the hard upshifts, and BNaylor's fix cured both. Hope this helps you!Good link for those with a 4T65E; but unfortunately, it does not apply to the 96 Century! It did not come equipped with the 4T65E. :shakehead

Yes, HotZ28 is right- I believe you'd have the 4T60E, and the fix suggested applies to 4T65E. Thought the 4T65E came out sooner than they did. Sorry for the bad info!