PHP files opening outside of Browser

For the past few days, every time I save or publish a post, a window pops up in my browser (Firefox) that reads,

“You have chosen to open post.php
which is a: PHP Script
from http://…
What should Firefox do with this file?”

I was able to live with it for a while. The buttons were working, they just weren’t going directing me back to the Manage screen the way WordPress usually does once you’ve published. However, this morning, I cleaned the cookies and passwords out of Firefox, and now I can’t get past the WordPress password screen. I put in my name and password, but the page doesn’t change. It just gives me that message, and when I reload it, it asks for my password again.

A Google search revealed that, in other blogging systems, this is a sign that the PHP hasn’t been set up correctly, but my website has been up since October and I have altered any major settings since I upgraded way back when.

Should I back up my database and reload everything, or is there a simpler solution?