That is a weird one. Something as simple as the shortcut for the add menu not working might be something wrong with your keyboard? Driver needing updates? Download Blender again just in case it has bugs?
Also be sure you are in the right context. Remember most of things in Blender are context dependent.
Also, knowing that mode changes can be confusing when one is starting out and can feel slow even later, I highly recommend installing the "3D Viewport Pie Menus" addon. It's included with Blender (with 4.2 you might have to add it from the Extensions tab). After that, ensure you have "Tab for Pie Menu" ticked under Preferences> Keymap. I also like to tick "Pie Menu on Drag" which makes it so just tapping the Tab key still flips between the last two selected modes.
Hope this helps make your experience with Blender less frustrating!
And something as simple as mouse cursor not hovering over 3D viewport will cause shift a not to work too.
Hi Rob, the quickest way to troubleshoot whether it is properly assigned is to open Preferences, go to Keymap, Key-Binding, and search all functions which use Shift A. It could be that you assigned this to something custom; it could be that something broke along the way without you knowing. This will show you all the functions across Blender where Shift A is specifically assigned - modes, editors, etc.
One thing that always got me in the beginning was not having my mouse in the right window. Make sure your mouse is in the viewport when you hit shift-A. If its in any other window it wont have the same results...or no results at all.
Also, as Martin said, make sure your hitting the right buttons...sounds silly...like the "did you unplug and plug it back in" sort of answer, but seriously. I hit Caps-A all the time.
thank you for all of the tips and help guys, it was late when I was doing it and dont even remember typing that haha!
iv recently moved from Microsoft laptop to a MacBook and im trying to get used to all of the changes. im sure its just small settings inside blender which need changing, I was wondering if its because im using the new version 4.2? I only downloaded it the other week, first time using the software and new laptop, mouse and keyboard
lol get used to it, it happens to me regularly , im convinced theres some matrix gremlin hitting hot keys while im working on stuff. one time this thing got clicked and it took me a week to figure it out 
