There are 2 positive wires that go into the 4 pin molex plug. If the microswitch goes bad, only 1 of those 2 wires will see voltage, and it will do exactly this. 

But yes, you need a good battery. if you run it without a good battery, and use a higher current charger, that portable board will end up on my autopsy table. 

Also there is a problem with the non-backlit models. the cap goo gets into the ceramic substrate of the Hybrid IC and it will cause all sorts of problems. Also, that flickering and shutoff means the 5V supply is starved for current. 

The regulation for the 5.2V B supply is, you guessed it... the Hybrid itself. You need to test the continuity of the 9Z30 back to the Hybrid, and make sure its connected .If it is, you have trace rot, or a bad Hybrid. Assuming your running this from a GOOD battery. 

Also the undervoltage lockout is around 5.8V or so on the battery. so 6V isnt quite enough. you need 6.2V or better on the B supply.