Can almost guarantee that it's the power supply. Many on this forum have reported the same issue with some small variations in symptoms but the constant is that the LAN connection is down. For example, on mine the SlingBox LED icon thingy stays illuminated constantly, and there's no network status indicator LED. Obviously it's getting power but not enough.
The remedy is to buy a new power supply / AC adapter. If your SlingBox is still under warrantee, it shouldn't cost you a penny.