The message that show up in the right corner keep showing a message box that says use USE to open the little envelopes. I don't see use so what key do I push?

You click whatever key use is bound to. To see what that is go to open up the pause menu, go to Options, then to Players and Controls, then to Customize Controls, then to Customize Buttons, then here you can see what key to press and bind it to something else if you want.

Okay, so I'll just have to basically have to reset it another key?

That depends. There are three relevant keys "use", "invoke netricsa" and "use/invoke netricsa". The default key binding uses the combined button. If you haven't changed your key bindings, it should be on the right mouse button. The combined key works as a use key if you press it once and opens the messages section with a double click.

It's very easy to open netricsa at inopportune times if you want to activate a switch, so I usually use the separate key bindings.

It just seems to pop up when I'm in the middle of killing a bunch of baddies. Then afterwards it won't let me open it up.

The pop up appears every time you've got a new message, e.g. when you kill an enemy type for the fist time. It has nothing to do with the display of the message. The message icon in the corner of the screen should still display the number of new messages.

I think you should open the key configuration menu and bind a key that's out of the way for "invoke netricsa" e.g. L if you play with WASD.

Okay, that's fine with me. I just want to be able to get to the messages with no problems.

Bump! I just installed the unaltered GOG version of Sam 1, and the button mapped to USE doesn't work. Tried rebinding it to a bunch of different things, but I could never get the USE button to work.

Game is broken. Anybody know what went wrong?

Don't call a game broken if you don't understand how to play it. USE by default needs double click right mouse button or Enter. You can go to player settings and set it so it needs just one click if you don't want to double click the button.