Yeah, the full reset or reboot might be your best option.
I'd try downloading a fresh copy and reloading the firmware, too. If you've never done it before, it's pretty straightforward and complete instructions are on the Canon website. You just need a clean, formatted memory card to do it, a full charge on the batteries and to carefully follow the instructions... most especially to not touch any buttons or turn off the camera while the firmware is installing.
To do the reboot, a "few minutes" with the batteries out isn't really adequate. Either leave the batteries out longer, perhaps an hour.... Or, while all the batts are out, turn the camera on and press the shutter release button once. The camera won't fire, but this should drain the remaining power from the camera. That's what's necessary to effect a reset or reboot.
After that, turn the camera off, reinstall the batts, turn the camera on and check the date/time. If they need to be reset, then you got a good reboot. If not, you need to try again.
Yes, factory reset also might do the trick, but usually just corrects incorrect settings deep in the menu, and this sounds more like a series of glitches.
All these are presuming there's something garbled in the software and/or memory that's in the camera, causing the problems you are seeing. We can hope, since it's a relatively easy fix that you can try yourself, at no cost.
But if instead it's a hardware problem or, as someone else suggested, moisture inside the camera... Unfortunately it's most likely going to need professional attention. Today's electronic cameras are highly complex and beyond most of us repairing ourselves.
If you have reason to suspect it's a moisture issue, you might be able to try yourself is drying the camera out thoroughly. Best way would be to put the camera inside a warm, dry, sealed place with a dessicant such as this
. Loose, single use absorbant silica can sometimes be bought at pet stores (it's added to cat litter) or plant nurseries (added to potting soil to improve holding moisture). And I have heard of using unooked white rice as a dessicant... Apparently it will draw off and absorb moisture rapidly, too... I'd only use the loose silica or rice very, very carefully, since to keep any dust out of the camera.
The problem is, if the camera got moisture inside (condensation, rain, splash, whatever).... particularly in a salt air environment... chances are there is corrosion on the electronics and circuits might have shorted out. Simply drying the camera out thoroughly might not put it back right.
I hope one of the simpler fixes works!
I can't help you, but I feel your pain.
