It all depends what is causing the "Red Ring" actually.
There are many causes of this sort of behavior around the XBOX 360 console.
If your screen is freezing, it may be that you will need to send the console in for repair to Xbox. However, odds are this is fixable. If you try all the troubleshooting steps I have in this post below and it still does not work, call 1-800-4-MYXBOX and ask a "Hardware" agent, REMEMBER THE NAME HARDWARE! If you get a Live, Media, Et Cetera they will not be able to help you unless they happen to be cross-trained in both. Once you call in, tell them your screen is freezing.
Go through the following Article...
http://support.microsoft.com/kb/907586/
and check for the following...
Make sure the clock is set right,if you are connected to xbox live you don't need worry about that.
Check disc for scratches, try without hd (Hard Drive). if freezes without the hd (Hard Drive) you need to call my friends at Xbox.
Also, make sure your power supply is always green. sometimes people have that if there in a surge protector.
Hope that Helps,
Sincerely,
Ex-Xbox-Tech-Support,
MurphyMAN