The distributor have a single o-ring on the shaft that contacts the cam. It's rubber, so it definately can deteriorate and stuff. Ultimately, oil in the distributor and cap.
It could be possible the arcing of the battery terminals created fault(s) elsewhere.
It definately wouldn't hurt to check the alignment of the timing belt as well. Like mine right now, I suspect my timing belt have jumped a tooth and possibly a failed timing belt tensioner. I haven't looked into it yet. The belt and timing belt is brand new from dealer less than a year old. Before this belt, I had a 6 month old timing belt I installed new completely lose it's teeths and snapped.
But check the simples first (wires and spark plugs) like
tashirosgt said.