when taking a picture the camera beeps three times and does not take the picture.

When taking a picture the camera beeps three times and does not take the picture. I have replaced the batteries.

Well the first thing I would ask it what kind of batteries did you replace it with? Often, underpowered batteries are just as bad as depleted ones. Many batteries such as AAs are general purpose batteries and are not designed for the high energy use of digital cameras and the flashes they trigger. As such, I recommend using high energy batteries designed for digital photography. Varta is a good brand. They are usually sold in camera shops, are long lasting (because they are sold in small quantities) put out alot of energy.
And, even though you think you've put in fresh batteries, underpowered batteries are just as bad. At the very least, make sure you are using Alkalines. Even better, batteries with a higher mAh - like around 2500mAh would satisfy the higher power requirements of your camera.

Secondly, I would do is reset the camera. This is a fairly easy procedure which involves either going into your setup menu and choosing "reset" (or intialize), holding down the menu key for 5 seconds, or, removing the batteries for a few minutes. It may be that the firmware loading got corrupted and the camera just needs to be "rebooted," which is something that turning it on/off won't accomplish. But after which, you should have the camera reset to factory default settings.

Another tip is to go to Canon's website and look for firmware updates. Download and install them.

If these steps fail to correct the situation, you may also have a lens that is out of alignment. You may need to send it in for a repair/service estimate. But understand that the average cost of a camera repair is around $180. As such, it may cost more to repair than it is really worth. The rule of thumb is that if the estimate for repair is north of 50% what you paid for it, you're better off taking that money and buying a newer and upgraded model.

Usually the 3 beeps on a Canon camera is indicative of the E18 error. Check out this site and see if it helps:
http://www.e18error.com/