Hi,
First, check whether the battery is full and its new, when the battery becomes older and cease to supply full power, you get the flash problem and White balance problems..
Secondly, check whether the camera is normal shooting mode, because in some shooting modes, Focus, exposure, white balance, will be loced and the flash will not fire, this is common...For eg: in Hi mode, flash is switched off..SImilarly you have preconfigured setting for each mode, ensure that you set it to auto mode before shooting
Thirdly, the flash icon keeps blinking or red light keeps blinking, then the problem you are describing is a problem with the flash charging indicator switch inside the camera. It seems to have failed and needs to be replaced
Fially try resetting the setting to default setting by chooaing reset default from the menu, it should restore your setting to factory default
If you still have problem, you can refer the product manual for your camera from the following link, it effectively explains the way to take clear photograph
http://www.olympusamerica.com/files/Stylus_1010_Stylus_1020_Instruction_Manual_EN.pdf
Please leave me comment, if you need further assistance
Rnj VINODKUMAR