Where can I purchase belts for a Pioneer LD-700 LaserDisc player?

You can check with the Pioneer store online. Here is a link to the manual that I believe you are looking for:

Pioneer Electronics USA Inc Parts Accessories Online Part Number VRB1120...

Good luck!

faulty belts in unit ?

Take cover off - check that a disc is not jamming. If problem persists get a new dvd player.

The dvd's are not spinning up correctly. If the belt inside is worn this will cause cd's to play but dvd's fail. open up and replce belt (small black rubber running on motor)

http://www.laserdiscarchive.co.uk/laserdisc_archive/laserdisc_manuals.htm
http://www.user-manuals.com/advanced_search_result.php?keywords=CLD-D503+manual&forward=plist&osCsid=fdea978e63ce5bba532e70fe9952444c

Check the power supply look for anything that might be burnt or damaged.

laserdisc would not play

Sounds like a belt is slipping.
wont open, wont close, makes clicking/grinding noises etc.
http://www.llamma.com/xbox/Repairs/thompson_dvd_tray.htm

You can also try flipping the player upside down and shaking it a little. I bought a DVL 909 and when it arrived the tray wouldn't open. The seller told me to try that, and it actually worked. I wouldn't recommend shaking it quite so much as this video shows... but it does show that it can work.

thanks