I'm using the same brand and model of router so there is hope.
I'll make the following suggestion.
Do things one step at a time -
1) Go into your router settings and turn off security - Choose 'Disabled' from the drop down list under the Wireless --> Wireless Security setting (you're just doing this briefly so it should not compromise your network.) Then see if you can connect the PSP. If successful proceed to step 2. If you are not successful here we need to investigate other settings in your router. One thing I would suggest is making sure you don't have MAC address filtering on. If you do have it on, turn it off and try to reconnect. If you want to leave it on you will need to add your PSPs MAC to the filter.
2) If you were successful with #1 go back into the router and turn WPA2 with TKIP-AES on.
Then make the shared key something really simple and short - like 123. I'd choose numbers because they are not case sensitive and there is less chance to mess things up. I have found that when I try to connect to my network with non-computer appliances it often takes several attempts because I have a long and complex shared key - getting it right can take patience and time on devices that do not have a keyboard.
If you succeed with #2 then you know you can connect and it simply a matter of getting the same pass key.
Let me know how things go. If you run into problems let me know where they are and I'll try to help.
Oh, one final reminder, make sure you click SAVE whenever you change a setting in your router and try to only change one thing at a time. A stepwise approach may tke a little longer but it leads to much less frustration in my experience. Good Luck.