It may be TRYING to lock up, but obviously isn't. If it were truly locking up, and slipping, you'd be slipping in other gears as well.

OK, I'll try a new TCC solenoid. I looked in a Haynes manual, and it said to bring the car to a service center. What kind of manual should I get that describes the process of replacing a TCC solenoid on a 95 Bonneville? Or are there instructions on the web somewhere? Thanks.

Most aftermarket maintenance manuals won't cover this. Chilton'* included. You'll need either a GM factory service manual available from www.helminc.com (and other sources....shop around for a good price, and don't forget Ebay), or an aftermarket maintenance manual specific to the 4T60E transmission.

If you've never worked on the trans before I would recommend taking it to a good tranny shop to have a good diagnostic done.

When i had to change my TCC selinoid on my 93 Corsica (V6 4t60E transmission) i believe it was around 30 bucks. But don't quote me.

I spent a lot of time looking for this but came up flat for the 4t60E transmission. I did find the tcc for the 4t40E but not sure if it applies? Once you have access to it its only one bolt and one wire harness to remove.