It does seem kind of odd that Monster cables would not work. I will say that Monster is usually overpriced- I am using a lower priced cable I bought on eBay and have had no problems at all.
As for using component cables the difference would be very slight- you may not even see a difference. HDMI is NOT required for Blu-Ray movies.
I would suggest finding a different brand of cable to try, maybe borrow from a friend just to try it out. If you like what you see and have no problems you will know what name to look for in the store or online.