I don't own an Xbox, but I know how common this is among Xbox owners. You should try calling the Xbox technical support.
From Wiki:
In the USA (check your documentation for local support), if the Xbox 360 owner does indeed have three flashing red lights, it is recommended that the owner call the local Xbox support line (1-800-4MYXBOX in the US) as quickly as possible. Upon doing so, a technician will gather the information required to send the consumer a shipping label and instructions via e-mail. The owner then packs his or her console (using their own box) and ships it via a courier with the prepaid waybill.[19] Within a period of 10-15 days, the repaired or refurbished 360 will be shipped back to the owner, sometimes in less than two weeks.
You can read the full article here, to learn more.
Since you're controller has been "compromised", I'm not sure Microsoft will replace it if it shows any signs of poor handling on the consumer's part, whether it be an accident or not. Regardless, I'm sure sending your console to the company (hopefully you kept the box) will be a lot cheaper than buying a new Xbox 360 altogether. I don't think it matters if you have all of the inserts that came with the system, i.e hardware instructions, offers from Xbox, the little baggies and twist ties, etc.
They will probably give you a bill, once you call them and provide them with a valid email address, which is where they'll send it. Not sure if you have the know the serial number of your 360 or not, but keep it handy just in case (should be on the bottom of your 360 or maybe on the box it came in).
Hope that helps. Good luck.