The way I do it is that I have a separate memory stick with all my "restoration" files on it so that when I put my Pandora Battery in it reads all the necessary information. I like to have Despertar del Cementerio on my memstick, I think the lates version is DC8. You will need CFW 3.52 or higher to run it so if you are on 3.80 then you are fine.
It sounds to me like your Pandora Battery works but you may lack the proper files on the memory card to get a proper boot. That is why it works when you have it plugged in without the battery and you get nothing when only the battery supplies power.
I assume that you have a good Pandora and only lack the proper memory stick, follow this tutorial:
http://psp.brewology.com/forum/viewtopic.php?t=9208
Read carefully and take your time.