tlvt,
I had this problem on my 1999 C5 coupe, which immobilized the car for five days while I was out-of-state. If water enters the computer compartment in the right foot-well, it can ruin the computer (water follows the wiring harness).
Here is how to unclog the a/c condensate drain:
It is located on the firewall, at the back end of the right engine head. It can be seen from above on the passenger side of the engine compartment, but must be accessed from below. The drain tube is a 90 degree rubber elbow, about the diameter of your little finger.
To remove the rubber drain elbow, raise the RF of the car (use jackstands...) while the engine is completely cool. Get under the car. It is a tight fit, but your hand can reach the rubber elbow. Pull it off the plastic nipple that protrudes from the firewall.
Clean the inside of the rubber elbow. The end is moulded into a small shape, about the size of a pea. Cut off the end to enlarge the opening. The rubber elbow will probably be clogged with white, crusty material.
Use a plastic zip-tie (non clasp end) to gently push inside the hard plastic nipple that protrudes from the firewall. That will dislodge any "goop" which is usually white, crusty material also.
Replace the rubber drain elbow on the hard plastic nipple, with the drain opening pointing to the ground.
This link will show you excellent pictures to help your repair:
http://forums.corvetteforum.com/showthread.php?t=1069597
You will have to remove the right seat (easy) and the carpet/pad (also easy) to dry. Make sure you dry the inside of the car with the carpet removed and dry the carpet/pad thoroughly in the sun.
Good luck.
