Disc Dive Lock
A PSP game will not load and play through the device if the disc drive does not lock closed. If a game is not working, check to make sure you hear the locking click of the drive when inserting a game. This can tell you if this is the only problem you are experiencing.
Firmware
The firmware running on your specific system could be out of date. Sony makes regular upgrades to its PSP firmware. If a new game does not work, it could be because it is not compatible with the firmware you are running. Visit the PSP website and download the latest version of firmware for the PSP (see link in References). There are easy-to-follow instructions on the website to guide you through the download.
PSP's Lens
If a new game does not load, it could be the PSP lens. Insert an old PSP game to check and make sure the lens can read the disc. It is possible that the lens got dirty or damaged and is causing games not to load. If the old disc will not play either, then the problem is not that it is a new game, but rather that the lens is unable to read the disc.
Memory Card
If a new game is not loading as it should, it may be because there is no room left on your PSP's memory card. Certain games require that small information files be saved before the game is played. If there is no room left on the memory card, a new game may not allow itself to load. Try to delete a small file off the memory card to see if this is the only problem preventing the new PSP game from loading.
Hold Button
If a new game is not working and no other steps have made the game load, the simplest answer may be the right one. On the right side of the PSP, a slide button can be set to "Hold." If the Hold button is engaged, certain functions, such as playing a new game, may become non-responsive. You may have accidentally bumped into the button and engaged it without knowing it. Slide the button off "Hold," and the new game should begin to play.