Ok, so I looked at your model and everything seems to be plain wrong:
- you add triangulate modifier at the end of the modifier stack, that does literally nothing to help the situation - order of execution is important
- topology is just wrong - overlapping vertex and faces
two solidify modifiers, two boolean modifiers (one unused)
ngons that just can't solidify properly
also boxes inside that cut have inverted normals (that doesn't affect the solidifiy modifier, but just so you know)
This is how your topoly looks like with your modifier stack:
One important note: solidify modifier after boolean is very likely to give you weird results.
You need to learn how to model simple shapes like this without booleans, I'm guessing it would take you less time than you spent trying to fix this solidify result.
You generally took the right path: simple shapes, then add (but not apply!) modifiers (like solidify, bevel, subsurface etc.) is a good way to model things like that - it really helps with quick modeling and further editing. But you must start off with clean topology.