You could try disassembling and cleaning the lens, and I think that could be a temporary solution. For a more permanent solution, try replacing the laser. You could replace the whole assembly - most probably a "kem450aAa". If the system is under warranty, Sony would replace it for free, but if it isint under warranty and you are good with electronics, you can do it yourself too. Opening up the system would, however, void the warranty, so be careful.
In most cases a beeping sound indicates a faulty dvd drive, and the fact that the disc keeps getting ejected, also points in that direction. So, I think you should replace the drive and see if it solves the problem.
One of the websites that offer MacBook repair is powerbookmedic. I think you can find the parts you are looking for and they also have comprehensive guides where you can see how to open and replace parts of your macbook. Some of things that could go wrong with the screen would be the screen itself, the logic board or the cables. Since you mentioned that it works fine with an external monitor, the logic board must be ok. So that leaves you with the problem either being with the screen or the cables.