TBH, WEP or WPA (in any of its guises) are all simply red-rags to the battlehardened WarDriver. If they want to hack your system, they will. WEP has been demonstrably cracked with google-y available apps in about 10 minutes (depending on traffic flow etc) and WPA2 with 256bit AES keys is the highest level commercially availabe (but not on the PSP or Livebox i think) but can take as much as 60% of the datarate in encryption overhead! so even with a (realistically unattainable) rate of 54Mbps, if 30+ of it is encryption, whats the point!!!
I genuinely feel that hiding your SSID and using MAC address filtering is as high a security level as is reasonable. Not being able to see the access point is the first layer that will prevent most casual leeching and the MAC address filtering gets around anyone actually using your bandwidth without your permission!
back to your problem tho, have you had any success with other wireless AP's? If so, it isnt your PSP, its the Livebox - my moneys on the Livebox! (but then i wont have a bad thing said about my latest toy - i luv my PSP!!)
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