You are on the right track, it would be good if you had a scan tool to see if there are any markers, the fact that you replaced the battery could make for the dreaded Catalyst not ready. I just had this with my son's 2000 and I did have to replace the front Catalytic converter with the CA legal replacement for $250. Once we did that only the EVAP monitor showed not ready, but that is allowable in CA so it passed no problem. But you should just drive it a bit and have it tested, like @phattyduck said " Seriously though, stop worrying. Drive it, take it in, it should pass just fine. If you fail, come back with your report and we can help diagnose. If you have any concern at all about tailpipe emissions, you can do a few tricks to help it along - even as simple as just keeping it running when you get to the smog shop and driving at least 5 miles before you go there. "

Good luck!