The easiest way to get to 3.10 oe-a is to use recovery mode...it seems like it takes a while/is hard, but it is really easy
This is how you do it:
1) Download this file located HERE
It is the folder used for the recovery option in recovery mode
2)Next download Dark_Alex's 3.10 OE-A
And the 1.5 Sony Update EBOOT
And the 3.10 Sony Update EBOOT
3)Next unrar the folders oeupmaker and oeupmaker% from the root folder to the GAME folder on your Memory Stick (X:\PSP\GAME)(X being your psp's drive letter)
4)Navigate to X:\PSP\GAME\oeupmaker\ (where X is your PSP's drive letter). Rename the 1.50 Update Eboot to 150.PBP and copy it to the oeupmaker folder. Rename the 3.10 Update Eboot to 310.PBP and copy it to the oeupmaker folder. (Make sure you put it in "oeupmaker" not "oeupmaker%
5)Now on your psp go to Game>Memory Stick> and run OE UpdateMaker.
6)Once it finishes connect your psp back into your computer and take the file called "DATA.PSAR" (located at PSP/GAME/OEUPDATEMAKER)
7)Boot into Recovery mode and toggle the USB (will be the first option)
8)Put the file that we downloaded in step one into X:\PSP\GAME\ (X being your psp's drive letter)
9)Put the DATA.PSAR that was made in step 5 into the Recovery folder we put in X:\PSP\GAME in the previous step
10)Exit USB and Select "Run program at /PSP/GAME/RECOVERY/EBOOT.PBP"
congratulations you should now be at 3.10 OE-A (If you did everything right)