From a plithera of posts on the forum about simular issues; most likely your power supply has gone caput. Simply replacing it should do the trick. You can order another one of of sling's site at http://www.slingbox.com/go/buy-replacement-parts , or buy a generic one with the same power output and connector plug requirements locally.
You can also verify the power supply is shot by checking it with a voltmeter for the correct output as follows:
The Center tip is Positive ploarity (+), while the outter connection is negative (-).
Power Supply: 6VDC/2.5A MAX
Input Voltage Range
100VAC to 240VAC
Input Frequency Range
50 Hz to 60 Hz
Output Load Range