My iPhone displays "Restore Needed" but won't stay up long enough to connect. A log shows CRC ERR

My 2 year old iphone 4 was around 38% battery when I closed my eyes. (TV nap)

When I opened my eyes, the apple logo was showing. It repeatedly reboots. If I use a wall power adapter I can get logged in and look around for maybe a minute before it crashes and starts over.

While it is up, no phone service is available. The PHONE icon has a huge red dot on it.

Online support database suggests charging it.

But the battery shows as 100%, plugged in.

If I remove the power cable, it immediately dies and is non-responsive.

Help!