My remote control does not work anymore for my JVC MXJ30 Stereo. How can I determine if I need to buy a new remote. The stereo works when I turn it on manually. However the CD player has stopped working. It says "No Disc" when one is in there.

There are a couple of things going on here.

The CD issue is, uh, common. They die. CD-cleaners are dubious at best.

http://www.repairfaq.org/sam/cdfaq.htm

For the remote, try this advice:

http://remotes.com/remotes/servlet/rs?=Display&contents=help_deadremote&uuid=A12954406270641

"Dead" Remotes Can Be Saved How to Re-Start Your "Dead" Remote Control
This only takes about a minute and will restart 1 in 3 "Dead" Original Remote Controls. Good Luck!
-----------------------------
Step 1- Pull the batteries out of the remote and leave them out until Step 4.
Step 2- Press and release each and every button one at a time on the remote control until every button has been pressed and released at least once!
Step 3- If your remote has slide switches, you must move the switch to each position then repeat the button pushing in Step 2.
(When you're done, be sure to put the slide switch in the correct position to operate the
unit the remote came with!)
Step 4- Put the batteries back into the remote, being very careful to install them correctly. New batteries should be used if you're not sure about the old ones.
Step 5- Try the remote.
Special Note:
If you have a digital camera, camcorder or camera phone you can test the remote to see if it is emitting a signal. Face the remote towards the lens of the digital unit until you can see the front of the remote. Depress any button on the remote. You should see a light (steady, blink or flashing) being emitted from the remote. If you do then the problem might not be the remote but the sensor on the unit.

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eBay has some RM SMXJ30J remotes cheap. This one will set you back $11.50 delivered.

http://cgi.ebay.com/JVC-RM-SMXJ30J-REMOTE-CONTROL-/120717037068?pt=LH_DefaultDomain_0&hash=item1c1b4bce0c