Engine operation seems to be the place to keep looking when you can.
Starting simple, and checking basics, will at least rule out some possibilities - and it's normal maint. you'd do sometime anyways.
1. Pull plugs, check deposits & condition, check wires & coil.
2.Run a compression test while the plugs are out for baseline numbers & to rule out mechanical issues.
3. A little deeper, consider checking cam timing - especially if the belt is getting a bit "old".
4. Off track a bit, check the serpentine & everything it drives to make sure things are turning smoothly - something to look at if it turns out your timing belt is due for replacement. Don't want to miss a possible issue by skipping right past it!
5. And anytime you happen to peek under the hood, just look at things to see if they look "right". Wiring connectors & routing, same for vacuum connections & lines, it HAD run right before - so we're looking for anything that might have given up the ghost or been damaged somehow....