iPhone Just Shuts Down

[oldimac]

iPhone v1 just shuts down and won't come back on until it is either plugged into my computer or my car charger. It is fine then and shows a full battery charge. I can make a phone call, visit the calendar, contacts etc.

Then out of the blue it just shuts down again and I have to either plug it into my computer or car charger.

I bought it in April 2008 as a refurb from the ATT store. It has worked flawlessly since until now. Is this a battery problem or something more serious? Anyone?

Thanks.

 

[SFStateStudent]

Have you done a hard-boot? (Hold down Home Button and On/Off Button until the silver apple appears and it shuts off; then press the On/Off button).