Problems?

This could be real simple or not. Kinda sounds like the trans is doing its job but the driveline isn't. The speedo is driven by the final drive, so the gears bout have to be working. Try high gear and see if speedo goes way up. Is there undue noise? See if a CV joint hasn't completely failed. If the lube you found is greenish and thick it's CV grease. CV's near failure usually pop in turns for awhile, then spit out the ball bearings that actually transmit the power to the wheels. After that, you're parked.