I had this problem and it turned out that my console was full of dog hair (she sheds a lot). My console was out of warranty so I just opened it up, disassembled the DVD drive, cleaned out all the hair with compressed air and cleaned the laser with a cotton swab dipped in isopropyl alcohol.
Considering the age of this 360, and the cost of out-of-warranty repairs, it's likely not worth it for you to get this particular 360 fixed via Microsoft - for that cost, you might as well just buy a new one.
There is, however, another option - fix it yourself. It may sound intimidating, but the fix isn't particularly complex, and requires maybe $15-$20 USD in parts. There are a few good guides if you Google a bit - here and here aren't bad, but there's a real famous PDF floating around somewhere (I'll take a look around and see if I can't find the name of it for you).
I've performed the heatsink-clamp replacement fix on four different RROD'd 360s, all successful. Especially due to the age, you're not likely looking at an E74 error, so you've got a fairly good chance this will work for you (and worst cast situation, you're down a little bit of money).
Whatever you do, please keep in mind that you can sell these for parts online - there are people out there who will buy these and fix them up, so if you're going to get rid of it, at least make some money to recoup the cost of buying another 360 new.
EDIT: As @Dave mentioned, don't forget to check the 360 support site. I've had numerous friends call me about RRODs, only to tell them to check all the connections to their power supply and have it start working again.
Best Answer
It voids your warranty if you open up the console. I've tried fixing an Xbox 360 myself by doing the X-Clamp replacement but that fix only lasted about 8 months before it red ringed again. Since Microsoft paid 1.5 billion dollars for you to have a 3 year warranty for your Xbox 360, you should just have them fix it for you for free. That is, assuming you've had this Xbox 360 less than 3 years.