Article from Squidoo
Make sure that the device is powered, connected, and used correctly
Before deciding to send the Xbox for repairs, make sure that all the basics are accounted for. The correct power button must be pushed. All the lines and connections to the internet and the audio video system must be working as it should. Inspect any physical damages that could be an indication why the device isn’t working properly. Burnt marks, dents, and other physical defects should be inspected if present.
Look for error codes
Xbox 360 could give you tons of error codes to boggle about. Think of an Xbox like a specialized personal computer system that is manufactured to handle and process game software alone. The box may show different error codes that will give you a good idea as to where the problem is. Examples are system errors, LED errors, and console reset errors. If you can, research the meaning of these codes so you can decide if you should take the box to the repair center or try a few more things with it. System errors are almost always the worst-case scenario. LED errors, on the other hand indicate a different set of message for every off, lit, or blinking light is shows. Consult your manual for proper documentation.
3. Open the carriage.
If you have done everything outside of the box and none seemed to work, you could stop here and just take your Xbox to the repair experts. However, if you think you have a good idea as to what’s causing the problem inside the carriage and has impeccable background on electronics, you can proceed to opening the Xbox chassis and continue the repair from the inside. Open the Xbox chassis according to the set guidelines. You won’t find the instructions on how to dismantle your device on the manual, so don’t bother to look for it. If you are not confident about looking for the screws, bolts, and locks that the Xbox 360 is equipped with, never mind the screwdriver and just take the device to the center.
Look for the damaged part inside
Rarely does the Xbox’s processor or motherboard get busted. But if they do, you don’t have much of a choice but to ditch the set altogether and get a new one. The processor and the board costs so much and repairing a broken Xbox due to these reasons is a little impractical. More often than not, the hard drive of the Xbox is the main culprit. Look for the hard drive and check if it has any physical damages. Without notable physical defects on the hard drive, the problem could be on the system files or software side. You have to use all your software programming skills to make your game console working again. However, reformatting the Xbox hard drive isn’t as easy as reformatting computer hard drives. You have to find the necessary files, mods, and firmware necessary to get the box working in its best condition again.