You have to perform two steps:
FIRST - Downgrade your PSP to 1.50 Firmware. You will need the downgrader, which can be downloadedr from the
Nooz Homepage (at:
http://www.noobz.eu). Considering your Firmware there are two downgrader choices (See below). Either downgrader pack contain ALL the necessary step by step instructions are in a
README.TXT file.
DOWNGRADER #1 - Get unpatched GTA:LCS UMD and 3.03 Downgrader or
DOWNGRADER #2Get unpatched Lumines UMD, upgrade your PSP to 3.50 Firmware, and then use the 3.50 Downgrader.
SECOND - Upgrade to Custom Firmware. Instead of 3.10 OE I suggest the latest OE CFW, which is 3.40 OE, or the newest 3.52 m33. Throw a search in
http://www.google.com for download links and tutorials. Again, within the Custom Firmware Pack you will find step by step instructions in the form of a
README.TXT file.
Hope it helps.