The LAN light flashes whenever data passes through the LAN port on the back of the modem. The transmit/receive lights flash when data passes through the satellite link.
Curiously, the LAN light flashes much more rapidly than the transmit/receive lights.
Power should always be on. Supposedly, it will turn a blood-chilling, soul-searing red when the modem overheats, but I've never seen it (my soul is intact).
System illuminates when the modem is in communication with HughesNet's ground center at the other end of the satellite link. It usually illuminates last when the modem is booting and it will darken first when an outage occurs.
There's more information in the manual (seriously, there's an HT1000 manual somewhere) but this is what I've observed. Flashing LAN is OK and means that your modem is feeding your computer the cat videos you requested!
~HF