Most xbox 360 RRoDs can be fixed with a heat gun. I bought a heat gun for $20 2 years ago and have been using it to fix 360s ever since. I have fixed at least 50 of them so far for friends and acquaintances, and in my experience a heat gun will almost always do the trick. I have above a 90% success rate, and have had my repairs last for almost 2 years (I repaired my main 2005 launch console almost 2 years ago and it just recently crapped out last month - so I fixed it again with my heat gun and sold it on craigslist for $80 with only the power cord and AV cord...then went and bought a new slim model).
Unfortunately the oldest launch consoles, which is what I had, have the biggest problem with heat and will RRoD again, guaranteed (the GPU is not effectively cooled by the stock fans and over time, with heating and cooling from playing the system and turning it off, weakens the soldier that connects it to the motherboard causing RRoD). Upgrading (or "modding") the fan so that it cools the system much better helps a lot though, and will greatly increase the life of the console...so I do it every time I fix a launch console.
If you dont know how to use a heat gun then I would suggest finding someone that knows how to PROPERLY use one as it is just as easy to fix your system as it is to break it by heating it up too much. If you heat it too little then it will do nothing, too much and you will melt the soldier completely, the balls under the GPU/CPU will glob together, and you WILL ruin it. You have to get it just right, and focus on the GPU, CPU, (H)ANA, Bridge, and RAM chips as those chips are usually the culprit. Most times it is the GPU though that will need to be reflowed with the heat gun. I also remove the X-clamps and use straight bolts and washers.
Almost every system that I have worked on I have gotten working. It just takes patience and knowledge of what you are doing. Basic knowledge of how electronic devices work helps as well.
Sure signs for an impending RRoD are if the system freezes frequently, if when you power on the system you get no video, or see strange artifacting on the screen (frequent graphics errors). Basically if your xbox 360 is acting up or doing weird things, chances are that it will RRoD sometime sooner than later.
A 3 red light RRoD is a backbone failure within the system meaning that something vital to the operation of the system has failed. You will usually get NO video output at all.
A 2 red light RRoD is a overheating issue which can be caused by overheating RAM most commonly, or even due to improper repair.
A 1 light RRoD is another form of RRoD where you will still have video output but you will get a black screen with a bunch of white writing on it and an error code will be displayed at the top (usually E74 is the most common, followed by E68).
It is also possible to have a RRoD with no lights. The system seems to boot properly and give green lights but you get no video. This means that the system is RRoD'ing but does not recognize yet that there is a problem...so it still allows the console to boot.
Any of these problems can be fixed in under an hour with a heat gun. Do NOT do it yourself if you dont know what you are doing unless you are willing to risk ruining your system in an attempt to fix it. There are tutorials on You Tube that I have seen - some are good and some are VERY BAD and if you dont know what you are doing, you will not know which tutorials will ruin your system (there are some complete morons out there who make you tube videos). You cant blame anyone but yourself if you try to fix your system and end up breaking it even worse.
Feel free to ask me any questions if you are having difficulty with a repair. I will try to get back to you in a timely manner, but I do have a life and dont just sit in front of the computer all day long...so dont get mad if you dont hear back from me immediately.
I repair these things professionally for $35 a pop, so if you are in Bellingham WA, hit me up and Ill fix your system for cheap (I could charge more, but I try to help people out - I have seen people charge $50 to fix a system and not even do it right). I have fixed systems with my heat gun that people could not fix in the past with a reflow station. I am damn good with a heat gun.