So, this is legit weird. Same thing happens on my supergun.
Voltage is now 5.0V.
When I first start the game, nothing happens (LED stays lit). If I leave it on for a while like this, and then restarts it, it works.
If I play it again a short while after turning it off (like 10 minutes seems fine), then it also immediately works.
I wonder if some capacitor or something is going bad? That could _maybe_ explain it, if the cap takes a long time to build up the voltage or something?
Either way, very strange issue.