As my product has evolved my co-founder's skill set has become irrelevant. Furthermore, I've come to believe his efforts at this point are hurting our potential more so than helping it.
We are incorporated as a C-Corp each sharing 50% equity on a 4 year vested plan, each currently with 0% vested. We haven't made any profit.
I've offered to buy him out and continue as is but he's unwilling to budge. Therefore I'm wondering if I can quit the company and then restart it with the same business plan but with a new company/product name and entirely new IP.
Can I do this? I don't recall if I signed a non-compete, but if I did and he did also, can we legally come to an agreement to negate it?
Can you? Yes, can he sue with or without the non-compete. Yes. As partners the rule of law is a fiduciary responsibility to disclose what is relevant to the business. If you tell him what you are doing, I think its OK. You just can't be underhanded about it like saying, "just going to do something else now" then compete.
It sounds like your only way to get a good outcome here is to negotiate one with your co-founder. It is very hard to get a clear cut answer with legal matters as they are rarely clear cut.
Try and sort something out with your co-founder, it will be the best outcome long term, and will save you always looking over your shoulder.