Hi and welcome to the forum:
To be honest, it sounds like a power management component failure. Given the age of the camera - the T1i was released in 2009, it will not be eligible for service, and even if someone was willing and had the components, it would be cost prohibitive.
My suggestion is to check out the Canon upgrade program, where you can get a percentage off a new unit by trading in the old one. Alternatively, the second-hand market is awash with much newer DSLRs at good prices. Lastly, you could check out the Canon Refurbished site:
Canon Refurbished Cameras & Accessories | Canon U.S.A, Inc.
I hope this is of some assistance.
Did you look down into the battery compartment to see if all the contacts are clean?
Other than that, there's an internal problem.... on-off switch went bad or deeper electronics failed. Either way, Tronhard is right, unfortunately. I have a niceT1i with battery grip I got for free in my 50D-60D-7D-6D lineup and it is a nice little camera.
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