There is no such thing as a non-powered HDMI splitter. There are splitters that have their own power supply, and splitters that are line powered. The line powered ones take their power off the 5V line of the HDMI cable. Unfortunately, the HDMI specificaiton only requires the source device to provide 55 mA on that line. It wasn't intended to power splitters, etc. If the source device does not provide enough current, the splitter won't work properly, and the operation of the source device can be affected. Performance of line powered HDMI devices is pretty dismal. So, the first thing to do is get a splitter that has its own power supply.
Same thing goes for non-powered HDMI extenders. The best extenders used HDBaseT.
If you are using two line powered devices in the same system, it is no wonder they don't work.