Truck won't turn over after dead battery

I recently purchased a new family vehicle a couple months ago to eventually replace my 2007 Tacoma. During the first few weeks I was starting my Tacoma every week and taking it for a little spin. One night I left the ignition on which drained the battery. I got it tested and it was faulty. I purchased a new battery installed it and when I tried to turn it over it was cranking very slowly. My thought was the starter had gotten slightly seized up due to not being started regularly, but it was rotating slowly, not clicking. Mind you It been sitting through winter and we've had a lot of rain the last couple months. I don't have a lot of extra money to get it towed in and inspected, but after multiple attempts of turning it over and I noticed a strange smell which appeared to be coming from the starter which also may have been slightly smoking. The truck ran perfectly before sitting for in the month or two, so I just made the assumption that installing a new battery would fix the problem, but it didn't. It is a manual so I was considering push starting it and see if I can get it started that way and drive it around but I'm assuming that wouldn't fix the starter issue. wondering if a blown up fuse could cause this problem. Fouled plugs. It has a hood scoop which some water might have leaked through. Any thoughts or ideas are greatly appreciated. Thanks