Go o Dark Alex's website. His software is very reliable. I downgraded mine a few months ago and now using custom fw 3.10oe-a
i have mine psp upgraded to 3.40 oea check http://www.psp-hacks.com/category/10 there you can download all the firmware you need first you have too check which firmware you have on your psp
go too http://www.psp-hacks.com/forums/about39858.html there they explain everything you need to know 2 hack your psp and play homebrew games
You should go to http://www.lan.sh/index.php too. Very helpful tutorials there. Many hackers including Dark Alex post there.
I still have a 3.10 OE-A, to lazy to upgrade it lol, I do have a bricked psp, but all you have to do is install a modchip. There is a new one from psp-devalution (i think i spelled it wrong) looks easy to install.
Same, I am using 3.10 0e-a. I heard 3.10 and 3.40 are not as stable as 3.03, but I don't see any problems so far.