What you describe might be an electrical problem but could easily be mechanical - cold start problems can often be traced back to mechanical and carb set-up. It's always a good idea to eliminate the obvious things before going for the more difficult. May I suggest doing a thorough service before replacing the diode board.
Start by changing the oil
Then check in roughly this order:
- valve clearances
- spark plugs and spark plug gaps
- cables (throttle and choke)
- points gap (as Spo123 says, disconnect the battery before you remove the front engine cover)
- timing (better to do it with a strobe light with the engine running rather than just doing static timing)
- carbs - tuning and balancing. Do this last
- Did I miss anything there?
When you got the bike back on the road did you overhaul the carbs? New gaskets and o-rings, check all the needles, jets and seats? etc? The Bing carbs have separate main, idle and choke circuits - the idle circuit runs through the float bowl and has a tendency to collect crap. A 30 year old bike can collect a lot of crap in the carbs. Might be worth cleaning out the carbs and replacing the float bowl and choke gaskets (as boxerboy81 suggests) at the least.
All that is good maintenance anyway and won't be wasted effort even if it doesn't fix your problem.
If none of that works then several others have suggested electrical and other things to check. Don't forget that you can check the diodes with just a multimeter (if you search youtube you'll find plenty of videos showing how to do it). Replacing a faulty diode on the board can be done for about $2-$5 (again search youtube for how to do it). That's a lot cheaper than buying a new diode board. Diodes that are fried will often look fried, have you inspected the diode board?
Good luck and have fun.