my daughter found my old flash (20+ years old) and tried it on her canon T3i. It didn't recognize it and it never fired, but she tried the shutter button. Could this have damaged her camera even if it didn't fire? I have just given her a canon flash and her camera won't fire it, but mine will. If it did damage it, can it be repaired? Any suggestions? Thanks.
Unfortunately, it is entirely possible that it did damage the camera. Older flashes have a higher trigger voltage and that may damage the camera. It should be reparable, if that is the case, but it could be somewhat costly.
You can find a bit of an explanation for this online here: Trigger Voltage but it's a little techie. Suffice to say, your best bet is to contact Canon for your next steps.
The problem is that in old cameras, the flash sync was a simple mechanical switch. The flash would present high voltage DC, say 300V, across the switch. When you trigger the shutter, the switch would close, 300V would flow and it would flash.
Modern cpu driven cameras use all semiconductors, and most are designed for at most 5 volts. So an old flash can present 60 times more voltage than the camera can handle.
This potential (voltage) is present any time the flash is charged. If it was off, then there is no need to worry. But if the flash was charged, it could very easily fry circuits in the camera.