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Assuming that "blank" means the flash has stopped working then:
First, and most obvious: On most Canon DSLRs with internal flash the main set-up menu (Red Camera icon) will have a line item named "FLASH CONTROL" This can be set to "Enable" or "Disable". If you set it to "Disable", your flash will not work.
Second: Is your camera battery very old and is it fully charged? As batteries age their internal resistance increases. The battery may be able to produce enough current to run the camera, but may not be able to provide the (much higher) current needed to charge the flash.
If you are using a camera with an internal "pop-up" flash does the flash head pop-up? If not does the screen display an error message (typically "ERR 05")? If the head is not popping up, there is a mechanical issue that should be repaired by a camera tech. If the head pops up but does not fire (assuming the menu settings are correct and the lighting conditions for the shooting mode are appropriate), you may have an electrical problem.
If you are using an external, hot-shoe flash: Is it firmly and properly attached? Are the contacts clean? Has it accidentally been set to "slave mode" ? (see external flash instruction manual)
If all settings are correct and you still have the problem it's best to send the camera or the external flash to a qualified repair facility. Even small electronic flashes contain components (power storage capacitors) that may store electrical energy at lethal voltages even when "shut off'. Unless you are familiar with the unit, have experience working with high-voltage electronics, and know exactly what you are doing, you should not tamper with the internals of an electronic flash.
There are two common problems that often happen on the T2i, T3i and T5i pop-up flash mechanisms. If you are not mechanically inclined the preferred solution is to send the camera to a camera repair shop for service. However, the cost may be prohibitive and might be more than you want to invest in the camera. Both repairs are relatively simple to do if you have any mechanical skill, and are careful. PROCEED AT YOUR OWN RISK!
Common issue No. 1: There is a tiny interlock pin built into the hot-shoe that mechanically keeps the internal flash from opening if an external flash is on the hot-shoe. It's not uncommon for dust and dirt to get into the area around the interlock pin which keeps it from moving properly. Repair requires removing the spring clip in the hot-shoe and to get access to the tiny vertical pin (on the right side of the hot-shoe) and cleaning the area around it with a small swab.
Common issue No. 2: This one is more complicated and requires having a small (Phillips No 0) screwdriver. You must first raise the flash head. This can be done by turning on the camera, then pressing the flash release button on the front of the camera and then gently prying the head up using a fingernail under front edge of the flash head. Once opened, turn off the camera. Then remove the two small Phillips screws on the underside of the head (now facing forward). That will allow the top cover on the head to be removed. Then slightly loosen the screw at the pivot point that the flash head rotates on. This is a special "shoulder screw" that is the pivot bearing for the head. Loosening it 1/4 to 1/2 turn counter-clockwise will often allow the head to work properly. However, if the pivot is dirty you may have to remove the screw, clean the inside of the plastic flash arm, clean the pivot screw "shoulder" , lubricate by wiping with a paper swab and a tiny amount of silicone oil, and then re-inserting the pivot screw. Re-inserting the pivot screw means tightening it only enough to allow smooth operation of the flash head movement, not tightening it so much that opening is restricted.
Again: Attempting even simple repairs like these entails some risk of damage. If you are not mechanically inclined, it's probably best to bring the camera to someone who is qualified and experienced to do the repair.
While the disclaimers have been made, I would strongly urge that any repair be done by an authorized repair facility. Canon or shop, etc. Camera's are sensitive electronic devices and in many cases, disassembly and reassembly can sometimes require additional parts (ones you won't have). If the camera is beyond its service life, a new camera might be a wise decision. Camera's 7 or more years old are often costly to repair and parts for them might not be available. Canon offers an upgrade program in many cases. Check with them, you may be surprised.
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"...gently prying the head up using a fingernail under front edge of the flash head."
You really don't need to go that far as "Common issue No 2". You often can pop up the flash up by helping it. Keep in mind the camera stops trying to pop the flash up quickly. You need to be "helping" while it is trying to pop it up. Once you do get it popped up a tiny drop of WD40 or even a tiny drop or two of denatured alcohol on the mech will often make everything work as new. This is a common problem.