My xbox 360 isn't working, no red light either (see details)?

My xbox 360 won't read the games I put in, so what ive been doing is installing the games to my hard drive when, on the odd occasion, it reads them. Once I play them from the hard drive it works great but (I don't play it much) yesterday I bought LA Noire and tried to save that to my hard drive but it won't read the disc and tells me that it may be scratched or dirty and to clean it with a cloth but there is nothing wrong with the disc and when I try to play it not from the hard drive it will get into it a bit and then freeze and not work, I phone the Xbox customer support place yesterday and the guy thinks the hard drive is the problem and is sending another one out to me, could this be correct (it still doesn't read the discs with the hard drive not attached)?. What's wrong with it? Can it be fixed? How much will it cost?