Originally Posted by merryman

Now you have it running again, check the voltage at the battery with the engine running, if it goes over 15v at any revs, you have a faulty voltage regulator. Clean the old carb out yet again, something has blocked the new one, so you must have a problem with dirt or water in the fuel. If the plug is fouled again, drop the needle one notch and see if that helps or hinders. You haven't mentioned the choke, a common problem on 350s is the choke plunger stuck partly open, but not likely to occur on the new carb, could the cable be sticking?

If you still have the fault it could be the coil, CDI or trigger coil, although theoretically these can be checked electronically, I go for substitution, cheapest first.