Will not take a picture with the flash on

If you're up to doing the replacement yourself, you can order a new LCD assembly here. If not, you can take the camera to a reputable camera shop and have a trained professional do the replacement. A third alternative is to buy a new camera to replace the five-year-old SD750.

A stuck shutter is another common failure mode for digital cameras. The symptoms of a stuck or "sticky" shutter are very similar to CCD image sensor failure. The camera may take black pictures (for shutter stuck closed), or the pictures may be very bright and overexposed, sometimes with lines, especially when taken outdoors (for shutter stuck open). To confirm a stuck shutter, put the camera in any mode other than "Auto", and turn the flash OFF (you don't want to blind yourself for the next step). Next look down the lens and take a picture. You should see a tiny flicker in the center of the lens as the shutter opens and closes. If no movement is seen, then you likely have a stuck shutter. If so, please see this link for further info and a simple fix that may help. Pay particular attention to Fix #5A.

Press the flash button (right on the multiselector, marked with a lightning bolt) repeatedly to cycle through the various flash modes. To turn off the flash, select the lightning bolt in a circle with a slash through it. Don't forget to turn it back on later if you want it to flash.

Do these "stains" only appear on flash pics? Are they always in different places on each pic? If so, these are dust particles reflecting the flash back to the lens.

Can u disassemble cam?
Error is in lens.
After disassembling check lens moving motor...

Maybe you have the ISO set to a very high number. Set it to "auto ISO".

You can either erase the pictures or transfer them to a computer using the supplied USB cable or remove the flash memory and insert directly into the computer's sd card port.

Just remove the screws, than SLOWLY pull apart.

Here are some simple things to try first for a camera that won't take a picture when the shutter button is pressed, or with an inoperative flash. They won't work for every case, but they're worth a try:
http://camerarepair.blogspot.com/2008/05/simple-fixes-for-cameras-that-wont-take.html

There is a cold solder on the flash unit. If you want to DIY, here is a tips for your reference
How to fix a Canon SD750 with intermittent flash problem