Need some advice

Ok the alternator has gone bad. I replaced it but I am still getting the same problem. I have some new diagnostics though. I took it for a drive. Slow steady acceleration is ok. If I floor it the acceleration is good also. It is only a problem when I am in that middle section. I liken it to giving the extra acceleration to get up a hill causes the problem. I am thinking it may be a fuel delivery issue. The fuel pump is original to the car from what I can tell. Anybody else have a suggestion?