I have a problem of connecting the internet with a few good games like phantasy star portable 2, resistance retribution, or Socom Navy Seal Bravo Team 3, it said that the system software needs to be update but when I network update it, it said that its already updated.
Yep. You have Custom Firmware (CFW). You'll need a plug-in called PSNLover to play online and I'd suggest updating to 5.50 GEN-D3.
Turn your PSP off, turn it on while holding R, go to Plug-ins and change it to enabled. You'll be able to go online then.