You should probably just invest in a slim, i have 14 of the older style 360s that i have collected that have been baked, x clamped, flowed, wrapped in towells, heat guned, 2 were repaired succesfully with a heat gun 1 more still experiences intermittent problems.
Microsoft used the wrong solder when building them and fixing them forever wont happen, it will always be a coin toss. Take the plunge, buy a new one and keep the old one around for a back up.
You can look up how to check the trouble codes and what they mean, i cant remember off hand exactly but its 2 buttons and will flash a code to you, and if your lucky enough it could just be the power brick or just overheating, the overheating is best fixed by opening it and blowing it out with canned air, it is not possible to blow it out good enough without taking it apart.
Good Luck
---------- Post added at 04:56 AM ---------- Previous post was at 04:53 AM ----------
This will help.
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