Yep, I have the same problem on a Panasonic NV-MX8 "flagship" camcorder from 2001-2.
It's turned into performing a black magic ritual to get each MiniDV tape to play... sometimes recording a couple of minutes on a tape will then get rid of the stripes on "play", but they come back when the next tape is inserted to be copied across to the computer.
Other times it takes the "precision tap" on the side of the camcorder. When I get really cross the "unplug power supply and throw it in the carry case" technique even seems to work!
Hope you get your tapes to play - and copied onto a more reliable medium. I would keep copies of the video files on a hard drive, as the DVDs I have burnt from camcorder tapes have all started jumping or sticking after a couple of years. Digital memories, eh? So fleeting.... :-)