My Sony DVD/VCR player has suddenly started stopping the action for several seconds, then starting again. What's going on? Do I need a new player?

Have you got a cleaner and cleaned it?
You need to before it stops moving at all or you will have to send it to the repair shop or buy a new one.

Not the disc cleaner but the lens cleaner. Department stores carry them in the electronic dept
dvd cleaner : Target Search Results