This problem seems to be wide spread. There are some advises in internet. Here is one of them (which seems to resolve the problem) from here:

I was having the same issue on a Rebel XS - 3 years old, had been working fine...

Would not take photos on AF... just beeped, clicked etc...

MF it would take photos no problem (though I was not actually focusing)

I googled the issue and found lots of suggestions on trying different settings, cleaning the contacts etc... nothing worked and I was resigned to buying a new camera or new lens

Turns out it was the outer focus ring at the end of the lens that was stuck - which makes perfect sense as it wouldn't take a photo since the focus ring wouldn't move.

Try this. Set it to MF. Hold the very end of the lens - (this is what focuses the lens - the larger grip is the zoom) - give it a gentle twist to see if it unsticks.

If it does unstick, put it back to AF and try taking a picture.

Voila! No reason to spend any $$ at a camera repair shop or buying a new camera or lens! (though I have a feeling many camera repair shops have made a killing by just twisting the focus ring free!)

P.S. I find this in internet and never test, so be warned