A very common and easily fixed problem with both 40D and 50D (as well as 20D and 30D... maybe 60D).... is a dirty, stuck shutter release button.
The symptoms usually start out progressively with the camera having longer and longer shutter lag, but eventually they'll stop firing at all, even though the camera appears to still turn on and operate normally otherwise.
All that's needed is a cleaning of the shutter release button assembly. It's just finger oils and dust that have gotten into and accumulated inside that switch, which can be cleaned out. The proper way to do this is to have a repair tech disassemble the camera to clean it, possibly without removing the switch at all. A local/independent repairer can probably do the fix in about an hour. A DIY repair is to "flood clean" the switch with rubbing alcohol without any camera disassembly (via the battery compartment, with the battery removed and the camera upside down... info/illustrations online, but this needs to be done carefully to avoid some problems). If you have Canon's factory service department do the repair, they'll replace the entire shutter release button module with a new one (assuming they have the spare parts available), so the cost will be higher.
Not saying this is guaranteed to solve the problem... but just from your description I'd recommend looking into it. So long as the camera "powers up", you can navigate the menu, playback images, etc.... but just doesn't seem to release the shutter when you press that button, there's a a pretty good chance chance this is all that's wrong with it.
It's probably unrelated... With those models now being over five years old, you might want to replace the little silver "button" batteries in each of them. This battery shouldn't effect the camera's ability to take a shot, but it might not be able to retain correct date/time, and some other menu/custom function settings might be lost each time it's powered down. Those are very common batteries, widely available for a few $, usually need replacement every five or six years. (Note: More recent models such as your 7DII don't have a user replaceable date/time battery... theirs is part of the main circuit board, is a rechargeable that gets refreshed by the main battery, and requires a tech disassemble the camera to replace it.)
Some other things that "kill" those cameras, though most tend to show different symptoms:
- If the camera has a battery grip on it and won't power up at all, try removing the grip, cleaning the contacts between the grip and camera with a clean rag lightly dampened with isopropyl (rubbing) alcohol, re-installing the battery grip and making sure it's nice and tight. The earlier Canon BG-E2, in particular, sometimes just don't make good contact and can give intermittent power failures (replacing the rubber on top of the grip with something thinner can help). Later BG-E2 and E2N were better fitting and assured better contact. But even they could loosen while shooting, causing sudden power failures.
- If the BP-511/511A batteries those cameras use have been sitting unused for a long time, they may drain and not charge back up correctly initially. Even though the charger indicates the battery is full, it's not. The camera will only power up briefly, may take one or two shots, or even none, then shut down due to the low battery. Charging the battery, reinstalling it and draining it again... repeated several times... might bring the battery back to life and the camera to normal function. Or, if it doesn't, buy new batteries (generic BP-511/511A are cheap online).
- If there has been an actual shutter failure, you should see partially obstructed images and/or an error code from the camera. Eventually the shutter might lock up completely though, with similar symptoms to what you describe. Shutter failures are more common on 40D than most of the other models in that series. For some reason, a lot failed rather early. A failed shutter might be too expensive to repair, assuming replacement parts are available (they might not be). If so, the camera might still have some value and be sold "for parts".
- Another common problem is a bent "pin" in the Compact Flash memory card socket. This might cause symptoms such as you describe, but more commonly it either causes corrupted files, or causes the camera to only be able to take one shot, or shorts out the camera entirely (so it won't power up at all). From your description of the symptoms I think this unlikely.... still you might want to inspect the pins down in the memory card socket carefully with a flash light, just to be sure.
Note: No, "back button focus" setup shouldn't/can't cause this sort of problem. The shutter should still release, at the press of the button, whether using BBF or not.
A very common and easily fixed problem with both 4... (
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