"Finicky" DVD Players

I own a Sony DVP-S7700 and a Denon 1500. Both of these DVD players are VERY particular as to what and WHEN they will play certain DVD's. I have 2 computors with DVD capability , both of which will play these DVD's anytime. I have noticed that many times (when I buy a used DVD from say:-Blockbuster- that the DVD player will not recognize that there is a disk inserted or says that it cannot read the disk. I can sometimes get this "refusal" and later on it will play with no ploblem. What's up?. Do I have to buy an EXTREMELY cheap unit to solve this problem?

Thanks for your help

Steve