Hi, I have a 1992 Buick Century with a 2.4L 4-cylinder engine with 68,616 miles on it. It was running fine yesterday. Today I went to back up and I no longer have a reverse gear. I drove all the way to work in forward (10 miles) but get no reverse. What am I looking at here?? Thanks in advance
Wow, thats a rare bird… A 4-cyl century… If you have no reverse, the first thing I would check is your fluid level, make sure its not low. Second, play with the shifter and see if the linkage is out of adjustment (it may engage reverse higher or lower then the indent, its something you will have to play with). If its none of these, you lost the reverse band in the trans, no cure other then a full rebuild. Sorry 
I had the same problem with the 1978 Oldsmobile Cutlass that I owned from the time it was new until a month ago. I lost reverse gear, but since my driveway has a slope, I could roll out into the street and get going the right direction. At work, I could pull into a parking place so that I was facing forward and drive back home. This worked for the entire summer. After classes resumed in the fall, I had to push the car out of a parking place a couple of times because someone parked in front of me. I then had the transmission fixed The independent transmission shop dropped the pan and showed me the blown seals. I had the transmission rebuilt and drove the car 12 more years. If your problem is the blown seals, the transmssion will have to come out of the car for a rebuild. However, you may be lucky and find it is just the linkage that is out of adjustment.
There are quite a few things inside that transmission which would cause a no reverse condition. The only things you can check is first, the fluid level and second, the linkage adjustment. Everything else is internal and required removal and disassembly to diagnose and repair.
transman
Thank you all for your advice…