Hello and sorry you're having problems.
The black spot on your screen is a tell-tale sign of a failing DLP chip in the set- this chip contains thousands of tiny mirrors and they are prone to falling off. Each one represents a pixel, and when they fail a black dot appears on the screen. They will multiple until the screen is eventually covered.
To have this repaired at a shop is an average $450 parts and labor (about $225 for the chip), and if you'd like you can use the link below to locate a shop in your area:
Alternatively, if this is something you're looking to repair yourself, I will need more information from you, such as the full model number off of the back of the set, and also if there are a bunch of tiny dots, or one large dot that is growing?
Other than that, I'm sorry for the bad news here and wish there were a quick fix.
If you need further assistance let me know. Please do not forget to click at least a 3 STAR RATING, at the top of the page for my efforts. You can follow up at any time if needed.