GE TV turns on with sound but the picture is black or has fuzzy lines for approx 10 minutes, then the picture comes on and works perfectly

Many RCA/GE sets had troubles with solder connections around the tuner section of the circuit board. These would cause many different symptoms including your fuzzy picture. You can test if your set has this by giving it a whack. This will vibrate those bad connections and affect what you see.

If you or someone you know is comfortable doing electronic soldering, you can try repairing this yourself. Instructions are widely available on the Web (this was a very common problem). Here is one link.

If you're not up to this repair, a TV service shop should definitely know what to do. It may not be worth paying for a repair, though. Labor may cost $50 or more, and sooner or later you'll be replacing this set anyway when the picture tube goes bad. Maybe it's time to put the money toward a new set.

Hope this helps. Thanks for using Fixya!

IT IS MOST LIKELY TO BE ONE OR MORE OF YOUR COMPONENTS ON YOUR BOARD I.E. CAPACTIORS RESISTIORS AND OR DIODES THAT ARE BAD OR OUT OF TOLLERANCE.