torotoro,
Try this (from another site):
"I got mine to work by connecting the USB cord to my laptop, putting in the battery, and pressing play. It worked! And after that the camera turns on normally."
You can read the entire thread here:
http://www.amazon.com/Canon-SD750-Wont-turn-Help/forum/Fx1X2CGYGWU8J97/Tx1VAL54ZWEHK2N/1?_encoding=UTF8&asin=B000NK6INU
If that solution doesn't work, I would still try to get it repaired under warranty. I've been successful a number of times having my electronics covered even though they were a month or so past the warranty coverage date. Wouldn't hurt to try.