even though it might not actually be overheated, the console things it is, with all the messing around with it you must have damaged it or the components.
it can also happen if the xbox cant detect the fans on the system, the fans might work and be powered but the xbox doesnt know this.
im not even remotely experienced at modding or fixing these things so im not sure if its fixable, but i doubt it.
if i were you i would go for an arcade console. and use all your current stuff on that, unloess you fancy upgrading you hardrive (if you have one).
there is no differenece in the arcade and elite consoles. except what they come with