Check Case and Fan
Overheating can trigger a flashing red light so it's important to check your PS3 for this possibility. Start by making sure the fan ducts are clear and check them for dust buildup. If you see any, blow it out with compressed air or use a vacuum to suck it up, being careful not to damage the inside. When your PS3 cools down, test its fan by turning off the console from the back, or unplugging it, and turning it on the same way while holding down the eject button until the fan starts. It should run fast and loud for about 30 seconds. When the fan shuts down, listen for two beeps and make sure the standby light flashes red. If everything works as described, your fan's doing its job.
Check Hard Drive
A flashing red light can also mean a defective or loose hard drive. Check this by turning off your PS3, removing the drive and booting back up with the hard drive out. When your console finishes booting, turn it back off and re-install your hard drive, being sure it's making good contact. Now turn your PS3 back on and see if it boots normally. If it doesn't, you might need to replace the hard drive.
Check Motherboard
Heat is the enemy of your PS3's motherboard, especially when it alternates between hot and cold while it's in and out of use. The problem is with the soldered connections of the GPU (Graphics Chip) and CPU (Main Processing Chip). The solder softens when temperatures are high and it hardens when they're cool. Over time this can lead to cracks and bad connections. If you have a soldering gun and some silver solder, you can open your console and re-solder these connections if they need it.
Reset Unit
Sometimes a simple reset is enough to get your PS3 back in the game. To do this right you need to drain any residual power from your console's capacitors. It's as easy as unplugging your PS3 for just over half an hour and plugging it back in. You have nothing to lose and everything to gain.