Primary click works until you *touch* the trackpad

...then you can't left-click at all - mouse or trackpad, button or tap.

This just started happening with my MacBook Pro (3,1) running Mavericks with all its updates (10.9.5). Had the computer for years now with no problems.

If I use my Magic Mouse, it works perfectly until I even touch the trackpad. The pointer will still move (with both trackpad and mouse) but you can only right click (luckily Apple allows you to right-click on the Apple menu to restart the computer, then it all works again.) This also happens in the recovery environment and "guest" Safari-only user, so I'm under the assumption that reinstalling OS X won't help.

I've tried resetting the NVRAM to no avail. Taking the advice of another poster (Can't click with trackpad or mouse (OS X 10.9, MacBook Pro)) I've enabled Mouse Keys to start by hitting Option 5 times just in case the mouse's battery dies, but there's gotta be a simpler fix to this. The Magic Mouse was in the other room with no batteries in it when the problem first arose, and my battery is not bulging (tried taking the battery out and the trackpad still won't click.)

I'd prefer not to go to the local Apple Store because the people there were rude and just wanted to sell me a new Mac (not in my budget right now). No trackpad makes the laptop less portable, if I have to carry a mouse everywhere that's one thing but it shouldn't quit working just by touching the trackpad.