Your cabling might not be fully complete. When you add a splitter to your wall cable, it sounds like you sent one wire to the COAX input on the SB and the second wire to the COAX input on the cable box. The SB has a built-in tuner, but it will receive on that direct wire from the splitter only those channels that your cable company is transmitting "in the clear" over its wires. These channels include, by federal law, the local affiliaties of the national broadcast networks (ABC, CBS, NBC, ...) plus some local public service channels, plus pershaps some home shopping channels, religious channels, etc. And when you setup on your Slingplayer software that COAX channel, you should be using a "plain vanilla" remote and NOT the specific remote for your cable box manufacturer.
To watch one channel on the SB and simultaneously a different channel on the TV itself, you also need to connect cables from the OUTPUT side of your cable box to another set of input ports on the SB, and then the same type of cables from the output ports of the SB to the input ports on the TV. And for this second signal pathway, you would program your SB to use a remote based on the model of your cable box, and most likely you will have to connect the IR blaster cable that came with the SB to the appropriate port on the SB, and position at least one of the heads of the IR blaster cable in front of the IR window on the cable box.
Once you've done all that, then you CAN watch one program on the SB while the folks in front of the TV watch another. But, note that BOTH of you can not be watching at the same time signals coming from the ONE cable box. For both parties to simulateously watch any of the cable box-supplied channels, you would need one of those "dual-tuner" cable boxes, or two separate cable boxes.