Sticky shutter blades

Canon EOS cameras manufactured in the late 1980s to early 1990s have an internal foam bumper for the shutter curtain which deteriorates with time, breaking down into an oily black tar. The tar oozes down and gets onto the shutter blades, causing them to stick. This results in the shutter either failing to open altogether or opening too slowly, resulting in blank or unexposed photographs.
cleaning procedure. Take a cotton swab and put a tiny bit of isopropyl alcohol or lighter fluid on it. Don’t drench it - you just want it slightly moist. Rub the tip of the swab on the oily patch, back and forth extremely lightly. You don’t want to apply any pressure, as the shutter curtain is fragile and easily bent and destroyed. Keep lightly rubbing the swab back and forth until the oil is entirely gone. Alcohol is a weaker solvent and so it may take a minute or two of gentle movement to dissolve the oil. Remember to do both sides of the shutter - you’ll have to move the mirror upwards to get the inner side, so don’t get any fingerprints on it. The easiest way to do this is to set the camera into mirror lockup mode (assuming your camera has the ability) and starting the self-timer.
That should fix the camera for the time being. Of course, the foam bumper is still there and continuing to degrade, so you’ll have to do this cleaning every now and again unless you pay to have it replaced. How often depends on your camera. Mine has gone for a year since the last cleaning without problems.

I'd recommend it's time for a service by a Canon authorised repair centre. Shutters do require replacing periodically in any camera - if it's been heavily used, or is a few years old, it may be time to get the shutter mechanism replaced. If it's still quite new, it may be able to be cleaned, but I'd book it in with a service centre to get it checked out.