When the button goes red, and you attempt to restart it, do you see any on-screen Error messages?
Best thing to do, would be to take the case off, the motherboard out and replace the thermal paste on the processor and GPU. These have caused notorious problems as MS simply scraped a few pennies by not applying enough or using the thermal tape - both of which do as you describe.
The best replacement would be Arctic Silver 5 paste - as this has been known to fix this issue with great effect
