Fix me

Hello guys, I just made an account here since I figured you would be able to help me out. The problem with my iphone (3G, 8GB, 3.1.3) Is that while I was using it, and I would press the sleep button (or whatever) to turn it off, sometimes, when I tried to turn it back on, it was totally turned off, like I had held down the button to manually turn it off. So I would hold the home and sleep buttons, and sometimes, the apple logo would appear and my phone would return, other times, a white screen would show up, making me repeat this until my phone worked. So today, figuring something was wrong with the hardware, I tried restoring it. As it is restoring my 3.1.3, (I use tinyumbrella to do this; kicking it out of recovery mode after it has downgraded) it gives me a message about 75% of the way done saying [error 6], and it tells me on the apple website that it may have something to do with security on my computer???
I am so confused, and would really like to have my phone working again. Please, if anyone knows anything, let me know.
Thanks, your helps is appreciated, and best wishes,
Flavius

 

the logs?