No, you have to hang on to it because it's all the proof you have that anything is wrong. You can initiate a dispute through the PayPal software -- there should be a link somewhere, and you have to input the transaction number. It should be pretty simple; just follow the instructions. PayPal will then contact the seller as part of resolving the dispute, unless you wait too long to take action, after which point they'll just tell you you're out of luck.
I once failed to receive a product after making a payment for it, so I initiated a dispute through PayPal. They got no response from the seller either, but the seller had money in his account, so they took it out of his account and gave it back to me. He contacted me after the fact, basically to say, "Okay, it's a wash," with some excuse about computer problems. It was pretty simple and worked out okay.