Hello, S3Jondoe. I had the same problem an i thought that i was f*cked.
However there is a way!!!
But u will need a pandora's battery, which you can make using your psp slim battery.
There should be a guide on how to do it, look on youtube or there may be a *master guide* or w/e on this site.
after u got your battery done, make sure u have a USB cable or a card reader in your PC.
Then look for TOTALNewbie easy installer. After u download it, put your memorystick into your PSP and go to SETTINGS, FORMAT MEMORYSTICK. After its done, start the Easy installer and Follow on screen instructions, after it tells you to format(press Y then enter) You will choose from 5 options. choose #4. It'll take a bit but eventually will finish. after its done and u press enter an the MS-DOS screen goes away. Take your memstick, put into your PSP without AC cord or battery in. After u place your memstick into your psp, u then take your pandora battery and place it into your psp.(MEMORY STICK MUST BE IN THE PSP BEFORE U PUT IN YOUR PANDORA BATTERY).
Now, your psp SHOULD turn on by itself, and the WI-FI, and Memstick light should blink, also if u notice the screen will light up a little bit. Since you have a PSP slim *NOTHING* will come up on the screen. So what u do is, make sure your battery is in place and press the ----> X <---- button.
After u press the ---> X <--- button the WI-FI and Memstick lights should start to blink and they may even stay lit up for a few seconds. Thats normal. This procees should take around 2-5mins. After it has finished (you can tell by the lights not blinking after awhile) your psp should turn off on its own, if it does not, then press ----> X <----.
When your psp is off u then take out your Pandora battery, plug in your A/C (power adapter/power pack), turn on your psp, go to SETTINGS, SYSTEM SETTINGS, SYSTEM INFO, and u will see that you now have CFW 3.71 M33
Note* If the lights dont blink when u put your pandora battery in then u may have to recreate your memory stick(use easy installer again).
****Theres a step in the easy installer where it says to remove your memorystick and turn off your psp. EVEN IF YOUR USING A MEMORYSTICK READER TAKE OUT YOUR MEMORYSTICK ANYWAY THEN REINSERT!!
*********DO ***NOT*** TAKE OUT THE BATTERY WHILE INSTALLING THE CFW ONTO YOUR PSP OR ELSE YOU WILL BE IN A WORLD OF S*IT.