The PSP runs on an 802.11b network. If you are running your router exclusively in 54Mbps mode, that means 802.11g. I have found that even running pure 802.11g networks sometimes my PSP can scan them, but not connect.
If you are not running any security, you should be able to connect your PSP to your wifi network. Commenters on a previous answer mentioned you can (or cannot) connect to an unsecured access point. I have found that there is some credibility to this. I have had issues in the past, connecting to my own unsecured AP. It does not happen in all cases however, and I would suggest that you TRY WEP encryption, if you're currently using unsecured wifi. Specifically WEP because it tends to have the best success rate with PSP connections--again, this is just my experience. WPA has worked for me, but WEP tends to work more smoothly. Additionally, as a troubleshooting step, you may want to try "b-only" mode, if your router has it. I do not recommend staying in this mode, but some devices use mixed mode in an imperfect manner, and it can cause issues with older b-wireless devices.
The PSP's networking is pretty flawed, to be quite honest. There are a lot of (disappointing) shortcomings, in my opinion, but there is no real reason why your setup SHOULDN'T work, as is.
Good luck to you.