Jim...depending on your cable provider...the cable box isn't necessary to watch the channels. So you will need to split the cable before it gets to the box. The TV w/o the box won't have the same functions as the one with (aka PPV and Schedules) but it should still have the general channels.
First, try disconnecting the cable that goes into the cable box and then connecting it directly to your TV. If you can still watch TV without the box in the middle then you are in luck. Now you can put in a splitter and split one to your new TV and the other to your cable box.
Always remember (as many other people have said) use a high dB splitter (more expensive) and the shortest cables you need (less expensive
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Have fun! and enjoy the freedom of multiple TVs