I didn't visit the forum until yesterday so didn't notice your post. Thanks for sharing it with me, could be useful.
First what I did yesterday:
My new screen arrived and swapped it with the existing one (went easy, screen only fixed on one side with tape) and pulled it back together only to see that I forgot to put in the speaker.. Anyway I went on testing and all seemed well. I was able to play full level of Sonic whereas before it would certainly crash. Given your information, I shaked it and pushed the buttons hard to see if it crashed.. no it didn't!
So I opened it up again, put in the speaker and guess what... after some seconds after turning on it crashed again
I opened and pulled it together several times but the result was the same, it keeps on crashing sometimes it didn't boot up.
Maybe It could be the motherboard is loose, I have to say everything in the RG-300 does have some play also the battery but not so much it loses contact, but who knows...
I'll take another look at it this evening, I didn't notice anything that was broken of or so that could make the MB loose tough.
You say you pulled the loops outwards, with this you mean the contact points for the battery, like this: (green rectangle)
Kind regards and stay safe!