I don't have access to the design details for MER, so I can't answer your question except in general terms. My direct satellite experience was with the DSCS-III commsat. It had several things that would trigger safe mode, including loss of Earth lock (the most serious case) and excessive battery drain. For my satellites, safe mode meant shutting down just about everything but the TT&C subsystem. It continued to transmit telemetry so we could diagnose the problem and still accepted commands.

It's quite possible that MER was designed to enter safe mode if the current draw was too high or if the battery levels dropped below a certain threshold. They might have engineered it to turn off the telemetry uplink in the case of low batteries but they should still be able to send commands to it using a lower data rate through the low gain antenna. The news yesterday that it was responding with a beep when commands were sent is encouraging. One possibility is that commands got scrambled during the bad weather uplink, leaving the memory in a bad state. Another possibility is that an SEU or some other thing (like static electricity, as Gary suggested) might have corrupted the memory. It's possible they may be able to command the computer to reboot itself (the universal Microsoft solution to all problems). They then have to reload the software that was uplinked to MER enroute.

When it gets down to it, if there's anyone who has a chance of saving MER, it's the wizards of JPL. Those people are GOOD!