PS2 - PS3 converters are unlikely to work now as Most used cheap Cloned DS3 chips in the production.
Sony disabled most when they blocked cloned DS3s.
Others lost analogue stick usage which is needed for steering and accel and brake controll in GT5.
If your wheel used DS2 emulation for those controlls thats why its likely dead as the analogue mode is disabled.
Cheapest replacement is GT Driving force pro (second hand), then Driving Force GT.