I don't think it's to do with the battery per se but more to do with the contacts for the battery. Looking at the image you supplied it seems as though the contacts "weaken" and then completely give up.
- Clean the contacts on both the phone and the battery, put it all back together, power up and let it settle.
- Once it's fully running, unlock it so you're on your home page and then shake the phone around, tap the back of it where the battery is. remove the back cover and try it.
Hopefully, you shouldn't get any more problems after cleaning the contacts. If the problem persists then it may be an internal wiring fault for which it would have to sent back/away.
If so then I want to stuff around with some custom roms before it does!
What do you mean "stuff around"? Rooting and custom ROMs is like second nature to Android and Android users. I myself am an addicted flasher (wa-hey) of customs and always have my i9000 rooted and almost certainly running a custom ROM.
If you are interested, head over to XDA Developers where you'll find hundreds of Android phones accompanied with hundreds and hundreds of rooting kernels and custom ROMs.
One bit of advice though, make sure you fully read and understand what the developer says about the ROM and how to install before even thinking about installing the ROM that you're reading about.