That particular Ideal splitter will work fine. There is an internal diode in each output leg of the splitter to prevent back-feeding unwanted circuits. This allows
ANY of the splitter outputs to accept power and route it to the common port and on to the pre-amp.
My guess is that the particular splitter you used may have shorted out the power supply and it has now failed internally. However, since you also replaced the coaxial cable, it is suspect until proven otherwise. Therefore, remove the amplifier and the power inserter and test for any reception using only the cable and the antenna.