Tried beveling the corners, but they won't bevel

Most likely you have clamp overlap turned on. Clamp overlap works on the model as a whole. It just prevents things from blowing up. So if it blows up, just try dialing the bevel down.

The other 'classic' is so-called 'Double Vertices'.

Select all (in Edit Mode) by pressing A, followed by M > Merge > By Distance.

Can we see a screenshot of your selection while trying to Bevel the corners?
Do you have the edge selected or the vertex?

As mentioned it could be double vertices. A little more info is required to be sure of the problem and provide the correct answer.