The Short Xbox Diagnosis Answer List

Here is the short list of Problems and Solutions to fix broken Xbox consoles, if you are looking for an elegant answer keep reading the site a few exist.  If you want to just swap out the broken component and get up and running here is a list of every error and what is suggested to replace.  This is not an infallible list but should handle the bulk of problems accurately.

P: Any LED error (like it tries to boot three times then flashes red and green) or any Call customer service message EXCEPT Call Customer Service #10, 11, 12
S: Replace Xbox Mother Board and Hard Drive

P: Your Xbox cannot recognize the disk, AKA Dirty Disk Error or Call Customer Service #10, 11, 12 or DVD drive will not open.
S: Replace Xbox DVD drive

Infrequent exceptions to above

P: DVD drive will only open with manual eject via paperclip hole, but will close using eject button
S: Replace Mother Board and Hard Drive

P: Get Dirty Disk Error even after replacing DVD drive
S: Replace Yellow DVD cable (this instance is rare but does occur on occasion)

P: Xbox will not power on, neither eject nor power button respond, no sounds or lights from the Xbox.. 
S: Replace Xbox Power Supply 
(There could be other causes of the above condition but often the power supply is the culprit)

P: Xbox eject works but Power button does not or vice versa
S: Replace Xbox Power Switch Assembly

P: One or more game ports do not work. 
S: Swap ports 1 &2 with 3&4 if the problem travels with the swapped port, replace the port if it does not replace the USB Daughter Board