MacBook turns off when charger is disconnected
Around two days ago I was about to move my workhorse to the kitchen, to do some culinary research (read: how to boil potatoes) when my MacBook just turned off when I disconnected the charger. I've had this problem before, which went away after a short while by itself. I just pinned it down to magnets or magic. After a while of being mildly annoyed by it shutting down, I began testing the battery in TechTool, which gave me virtually no information save for the fact that the battery is just maintaining its charge, but not actually getting any.
The battery indicator shows a 100% charge, as does Coconut Battery, which should mean that it's not the SMC. I did an SMC and PRAM reset, though it's unclear if it did anything at all. I'll try an SMC bypass and see if that does anything at all and update on this.
Logic tells me that it's the I/O board which is fooling around, but given my current financial situation, I don't want it to be. So, bottom line, is there any way to be completely sure that it's due to the I/O board, and/or any good way to fix it? Any help will be very appreciated and will hopefully help others in the future too.
For the sake of clarity, I'll enclose two Coconut Battery screenshots for future reference.