If I understand you correctly, your Sony charges up completely from a wall charger and works fine as an EReader.
When you plug the USB cable into your computer, it connects for a few seconds and then drops.
What operating system are you using?
It does not sound like anything is wrong with your Sony, but that there is a USB driver problem. Possibly some other device's USB driver (WebCam?) is grabbing it and saying "Not in my town you don't".
If it were me, and I was running Windows XP, Vista, or 7, I would uninstall the Sony Library and Adobe ADE.
I would then install Adobe ADE from:
http://www.adobe.com/products/digita...?promoid=DTEIO
That by itself should let you connect to your Sony, as it includes a USB driver.
If that works, install the Sony Library. Or just use Calibre.
Robert