Yup I'd have said similar. Sounds like the starter motor and engine haven't disengaged from each other. I've always been told to shut down immeditatly if either starter motor warning light stays on OR oil pressure doens't start to rise immediately after starting up, and 20 seconds is a long time in my book for the light to stop on. ( I was thinking about C150s but I imagine most a/c are the same)
I'd shut down and collar an engineer to have a look, or tell the club your renting off you want a new plane.