Have you tried disassembling the motor to see if it's just corrosion on internal connections or are the brushes worn out, etc
You can pull the motor from the door, don't forget to tape the window glass up to hold it in position in case it wants to fall after removing the motor, and disassemble and test on the bench. Much easier than messing with it in the door.

Morads has a couple for 79.00 shipped.
http://stores.shop.ebay.com/Morad-Parts-Company_Buick-Riviera-1995-1999_W0QQ_fsubZ13482291QQ_sidZ38997246?_nkw=window+regulator&submit=Search

I always email them and offer less and they usually go for it.

I found it on Monster under Electrical , Body electrical ,Front door ,Window motor - Window motor, aurora, riveria, left $101.20

Wouldn't that be better than used? The used part could have more miles on it than the one I've got.

I'll take it apart and look at it. While it's a sizeable motor it looks like a basic cheap as crap brushed motor. Can you get the brushes for these?

How do you tape the window up? There's no frame to tape it too

Yes, I would get new also for that price.
I forgot about the design of our window / body lacking a window frame.
Is your window currently in the UP position, if so when you remove the motor be careful to hold the glass and try to let it go down and rest on the bottom of the track's travel.
Just wanted to give you a heads up to be careful with it that's all. It might not try to fall down on you, I don't know for sure. You'll just have to see how it reacts.
You might be able to find the parts to rebuild it, but it's not worth it if a new replacement is only $100.00

Wouldn't hurt to price it from the dealer...

Yeah, it's up.

Shouldn't it lock into position? It doesn't sound like good design to have the motor supporting the weight of the glass.

I may lay off of this until I know I can have the car down for a while again, just in case.

Once again, Rick is absolutely right... There is a counterbalance spring, as I mentioned originally, but the motor assembly is self-locking. It is a worm-gear system - easy for the actual motor inside the assembly to turn, with high torque multiplication, but it cannot be turned in reverse (from the output shaft.)

Use something to prevent the glass from dropping when you remove the motor. After that, you can lower the glass by hand until it equalizes with the spring, and then attach the new motor.

I have an inexpensive tool made to hold the window when replacing regulator assemblies. It consists of two suction cups attached to each other by a cord.
On a window with a door frame you put one suction cup on the outside of the window and the other on the inside with the cord going over the top of the frame and it holds the window in the up position. I actually got two of them for extra insurance.
On a car without a door frame, like the Riv, you can put the suction cups on the window glass (outside) and the others on the roof of the car to hold it up. But you have to be able to remove the motor with the door closed and work from the inside.
This is where it helps to have second person holding the glass for you while you do the swap with door open.

BTW JR, what happened to the pictures that were in your sig?

Alrightey, will start looking for suction cups. I'll put 'em on a rope and throw it over a rafter so I can work with the door open.

About the sig pics, I decided to take them down while AA battles GM's corporate lawyers. Better safe than sorry as they say

Hmm, came back from TN and got in my car and tried to roll the window down, nothing. Whatever I drove some a tried it an hour later and it rolled down and worked for about a week. Today it's not working again. I can hear clicking in the door. Is this likely the switch, motor, or something else? Passanger window did this as well recently.

Sounds like what happened when my motor was going out. Acted like that for a couple years.

So you could hear it clicking inside the door?