If the clock doesn't work, the rotor with the pinion that turns the gears could be frozen. If you're handy and you can access the clock, you can find a replacement rotor on eBay, etc. I don't think the smaller types of rotors GE/Telecrhon switched to in the late '60s (the "S1" type) can be revived like the older, larger ones ("H3" type).
From what I've read here, the "Sensi-Temp" burner controls are no longer made. You'll have to keep and eye out on eBay for one of those, too.