Typical of Canon pop-up flashes. There's a microswitch under the hot shoe that prevents the flash from popping up when a shoe mount flash is attached. This can get dirty and stick, preventing the built-in flash from working.
It's a long recognized flaw with Canon and has been around even before digital. Canon apparently refuses to admit there is a problem and continues to use the same design. I've had six Canon cameras with built-in flashes, two film and four digital, and each has exhibited this behavior at one time or another.
The fix entails removing the little sheet metal plate on the hot shoe and gently lifting the pin in the switch and then replacing the plate.