That is what happened to mine. Mine would play for maybe 5 minutes and it would go Red. Then it would start descreasing and it would never work again. Also, if it is 4 Rings that are Red, then don't worry, that just means that you plugged in the wrong cable somewhere, which I can see hapenning on a big TV like that. If it is 3 Red Rings, I can't help you, so if you have a Best Buy Warranty(luckily I had it) you could get one in the same night, or send it to Microsoft and get it in about 5 Weeks.
Additional Info on Red Rings:
Three flashing red lights
When a Microsoft Xbox 360 console experiences a "general hardware" failure or "core digital" failure, three flashing red lights appear (known as the "Red Ring of Death") around the power button, in lieu of the four green lights indicating normal operation. Warning signs may include freeze-ups, in which the screen has strange, spontaneous graphical problems in the middle of gameplay, such as checkerboard or pinstripe patterns on the screen, the sound is frozen and changed to a strange, static-like sound, and the console only responds to pressing the power button to turn it off. The console may also say that the disc is unreadable, this may also arise from issues with the consoles power supply. These events may happen once or several times until the general hardware failure occurs, when the user attempts to turn the console on, and the three red lights are seen and the console will not function.
Some have confused General Hardware Failure with a similar looking error warning where four red lights appear, in which case the console does not detect an AV cable is plugged in.[5] The four lights can sometimes also be seen when power surges or very brief power outages occur while the console is running, in which the console needs to be unplugged and plugged back in again to reset the error.
In the USA, if the Xbox 360 owner does indeed have three flashing red lights, it is recommended that the owner call the local Xbox support line (1-800-4-MY-XBOX in the US) as quickly as possible. Upon doing so, an Xbox representative will gather the information needed to send the customer a package label by email. The customer packages his or her own Xbox 360 and takes it and the printed out label to a shipping store, where the emailed label is exchanged for the actual package label, and it is shipped to the repair center. Within a period of 2-10 weeks, the repaired, refurbished, or in some cases, replaced 360 will be shipped back to the owner. [6]
[edit] General hardware failure
Another general hardware failure is shown by one flashing red light, and error codes E 74, E 79, or E 71 displayed on-screen. This can occasionally be fixed by ensuring that all A/V connections are securely attached. However, this error is often a result of a hardware failure that is not consumer-serviceable. These hardware failures are not covered by Microsoft's extended 3 year warranty.
[edit] Response to rate of failure
In the early months after the console's launch, Microsoft stated that the Xbox 360's failure rate was within the consumer electronics industry's typical 3% to 5%.[7][8][9][10] Nevertheless, Microsoft has not released their official statistics on the failure rate of the various versions of the console; the company's press relations policy is to focus on the prompt resolution of any technical problems.[11]
On July 5, 2007, the Vice-President of Microsoft's Interactive Entertainment Business division published an open letter recognizing the console's problems, as well as announcing a three-year warranty extension for every Xbox 360 console that experiences the "general hardware failure" indicated by three flashing red LEDs on the console.[12]
One possible cause of the General Hardware Error is cold soldering. The added mass of the CSP chips (including the GPU and CPU) resists heat flow that allows proper soldering of the lead-free solders underneath the motherboard. This causes cracking and voids in the solders themselves from prolonged constant temperature changes inside the console. Lead-free solders, however, might be the cause of this because, when properly soldered, they take on a dull appearance that professionals take as a cold solder joint in older methods, thus leading to confusion. Lead-free solders also require a greater amount of heat (213 degrees celsius) to solder properly when compared to older lead/tin solders (185 degrees celsius).[13]
A source that has been identified as a team leader and key architect in the creation of the Xbox and Xbox 360 and a founding member of the Xbox team[14][15] provided insight as to the high rate of failures. The interviews suggest that Xbox 360 units that fail early in their life do so because of problems in the system design, parts supply, material reliability, and manufacturing issues as well as a system not tolerant to faults. These issues were alleged to be the end results of the decisions of management.