Some splitters work with remote power i.e. they take their power from one of the output lines which makes life easier if there are no sockets in the loft or wherever you put the splitter. This means there’ll be a box somewhere that needs to be plugged into one of the aerial sockets in the house and turned on.
Another thing to check: is the splitter wired up the right way round? If they had Sky, it’s possible they were using he aerial cables to distribute the signal from the Sky box around the house, in which case one of the rooms might be plugged into the input of the splitter.
Oh yeah, and check the leads that you’re using. When I had a similar problem I wasted a lot of time because one of the cables I was using to plug the TV into the wall socket was duff.