I just had the same problem with the passanger side. Sounds like your control module is bad (seat control thingy). Although you might want to check your fuses first. I was stumped with this until I checked all power with volt meter. Power was making it to the motors but the "module" was not engaging. The circut relay was dead. Needless to say I had to replace the control unit for a $140 (you have to buy part from Volvo). Drivers side Im sure is much more expensive becasue of memory function.

Replacement is easy, just remove the control buttons and remove the plastic cover from the rear of the seat forward. Take apart the module and disconnect the power feeds. Put back toghether in reverse order and youre done.

From what I understand this is a common problem. Good luck.