I replaced the battery and thinking the logic board might be my next step. Currently, my MacBook runs fine when plugged...

Really, it all depends on what year of MacBook you have. Yes, getting a recent model logic board is expensive. And, there are many places that sell refurbished logic boards with faster components than our current model. I suggest doing a thorough search of components for a DIY setup if you're out of warranty, don't want to pay for a new machine, and have a knack for unscrewing the cover off and unplugging some wires. Ifixit has some great tutorials.

Actually, it's very economical. You can replace the logic board for roughly $200 along with your processor. Drive your computer into the ground, then replace the logic board with 8gb and it's like having a brand new machine.