Erm I'm no expert, but first things first is that your firmware is old. You should be on 3.90 M33 at LEAST! 5.01 M33 is the latest.
Here is your error:
sceNetApctlConnect error returns
SCE_KERNEL_ERROR_LIBRARY_NOT_YET_LINKED - 8002013A I think you may have modified your PSP in some way. Since 3.03 OE - C is regarded as the "modders firmware", I'm not surprised!
I think you should upgrade to 3.90 M33 and try it there. If it works, use the network update to go to 5.00 M33.
If you have 3.03 OE - C because of your themes. Then install the latest CFW and install CXMB instead. It's a PRX plugin that allows you to run a theme without modifying the flash0 at all! 4.01 M33 has a bigger selection, but the 5.01 M33 list is growing!

Here's also a list of all 4.01 / 5.00 themes. Take your pick!
http://trobert94.saina-lesite.com/NOTE: On the site go to "Options" tab and select your firmware.
I must admit the site I posted is very good. Download for CTF, Flash0 and screenshot files! Better still it doesn;t go through a 3rd party server. The downloads are quick, clean and simple. No typing codes!

Don't you hate those online servers?
G65FJ --> Download... "Sorry wrong code entered". Grrrr

Hope that works and have a good day!
Angelo