The link by ektoric aptly provides the solution.
However, the current state of affairs has advanced.
The cause of the current users having the problem is that the Clock battery has discharged while setting on the shelf. This brings into play the Q2D06 problem since the time is 0 (not initialized).
The solution is to set the time via the internal serial port and load the latest software (10.1.3 or later). The clock battery is a rechargeable type and recharges when the XO is powered on (even though it does not boot). It takes about 4 hours to fully charge a fully discharged clock battery.
A USB to serial adapter for setting the time is available from ilovemyxo.com for $ 2.00 (plus shipping).
So, the solution is get the adapter, do some minor disassembly, set the time using the adapter and a PC computer as a communication terminal, and install the the latest software. If you are up to this, then there are detailed steps (and link to Anna's disassembly video) at http://xoshare.org/mi
, which provides key links to OLPC wiki references.
You can also contact one of the repair centers for repairs. The Mid-Michigan center may also loan you the adapter (with drivers for PC) and USB flash drive with the latest software (for clean install).
Choose your poison