Apple logo keeps turning on and off

Hi, When it ook it home last evening and plugged it into the charger — POW, it came back on. It worked just fine for as long it is was plugged in but when I unplugged it it began the usual cycle of turning on and off. I've had this iPhone 3 for two years now and it's never been opened. I've dropped it a whole bunch of times though. Unlike many other phones, the iPhone battery cannot be disconnected by the end-user (and you all probably already know that). Could it be that the battery is weak and the phone realized that after I assembled it all back together? The battery was working fine before I disassembled it. It wouldn't hold charge for very long time but it wasn't like this either.

Could this be a cable issue or something?

I also forgot to mention, the battery was glued to back and it was glued hard. (I dunno what they use but it must have been troll snot. :p) The battery seems to be a little soft around the edges. I followed the instructions on iFixit and removed the battery as instructed but it did get a liiiiitle bent when I tried to pry it up with the spudger. Could i have messed it up?

I have a voltage meter with me — could you shoe me how I can check the batter voltage? Can I even do this?

Could be! Check the battery with your multimeter- should be 3.7?. Put electrodes on contacts