If we presume that both TVs work OK and you know how to tune in the second TV... then your problem could be the cable, the splitter or just that the 2nd TV isn't getting enough signal.
Do some basic trouble-shooting...
1) swap the TVs. Do they both work OK on the good signal cable? Do they both not work on the bad signal cable? If yes on both counts then it's a problem with the cable or the splitter.
2) what happens if you swap the outputs on the splitter? Does the problem move with the splitter socket (if so it's probably a dodgy splitter) or stay where it is?... (could be a cable issue or lower sensitivity of the 2nd TV tuner)
If your splitter looks like this
then it's not helping your system.
The TV tuner needs a certain level of signal to work. Most decent outdoor TV aerials provide enough signal for the TV to work fine when properly installed. If you need to have a booster on yours then you're starting with a handicap. Using one of these passive splitters is going to divide the signal in half; 50% to one TV and 50% to the other. Your 1s TV might just be OK with that. The 2nd TV might not. With analogue (the old style 4 or 5 channels before Freeview) you might have got a bit of a snowy picture with less signal level. Digital is more fussy. Not enough signal = no picture at all.
Either get a new powered booster with more than one output or have the TV aerial looked at. Short term the booster is the cheaper option.