A large black circle appeared at the top of my TV screen. I powered it off and unplugged it for several hours; Now the circle has bled a teal blue color, and coloured lines have formed running straig

SOURCE: theres a line threw my tv.

It has a problem in the vertical sweep circuit that puts a nonlinearity in its output and you see the glitch in the normally gradual sweep as a line. Since a hit upside the set seems to help, you should just resolder the whole vertical circuit area (doesn't take long) and see if that cures it. If not, start replacing the electrolytic capacitors in that area.
Hope Ya Fix It!

SOURCE: line across top of screen

If the picture is ok otherwise then only thing that probably needs to be done is a vertical height adjustment. That is if the lines never changes position from cold to hot.

SOURCE: TV Keeps flashing Fuzzy black and white static then the picture appears

The half picture is a verticale problem. This is difficult to repair. Send to a repair shop.

SOURCE: DLP HL-R5067W

Your model has a maximum resolution of 720p. What you might want to do is make sure that both your cable/sat box and game stations are outputting at no more than 720 resolution. It's easy to assume that all HDTVs may accept a higher signal, and while they might, some of the scene changes or handshakes may make that operation cause the symptoms you describe.

SOURCE: Intense white & coloured horizontal line on black background on startup

I wouldn't attempt as the capacitors on a tv store around 25000 volts this is more than enough to kill you and they keep there charge even when the tv is off. Either take it to a repair shop or put that money towards buying a new tv - Do not even attempt to open the tv. (It sounds like maybe a tube has gone or the electromagnet that makes the beam move vertically is gone.