You used the term "router" to describe what you tried that didn't work. If that's what it really is, I suspect it was a "router" intended to connect to a cable or DSL modem with WAN port, firewall and multiple LAN ports. You could possibly make that work, but trying describe how to reconfigure it as an unmanaged switch isn't feasible in this forum. A "switch" and a "router" are two different things.
Get an Ethernet "switch". A simple, consumer, 5-port gigabit switch is dirt cheap now; less than $20. Beware of "Fast Ethernet" which are still around for about $10 or so. Fast Ethernet is 100Base-T, not Gigabit (aka 1000Base-T), and it's not considered "fast" any more. They're obsolete. Connect an Ethernet cable from the Ethernet powerline adapter to the switch, and one cable each from the switch to your two devices. On a 5-port switch, you'll have two ports left over for more stuff, and the number of things wanting to connect to the Internet never goes down. On a true switch, it won't matter which port you use for the incoming from the Ethernet powerline adapter, and which you use for the game box and which you use for the other device (TV ?? computer ??). Do NOT use a "splitter". I'm amazed those things are still around. Must be a vestige of the USOC analog telephone systems (four-line analog telephones using 8-wire cables with the same RJ45 plugs and jacks). Ethernet cannot be "split" like analog phone lines using a 99 cent splitter. The two are completely different technologies.
Observation #1:
I used the Ethernet powerline adapters in the past. They usually work, but they're not the best. As you've experienced, their throughput (data rate) isn't very fast. Depending on the power wiring in the home, they're sometimes extremely unreliable or don't work at all. I had nothing but headaches with the two pairs I tried to use in my house and finally set up a WiFi mesh. Your situation is not uncommon with a WiFi AP at one end of a home and near zero signal at the other end in a bedroom, especially when they're on different floors. There's a tendency to want to WiFi everything versus hard-wiring Ethernet cable as much as possible. WiFi is half-duplex and only one device can be transmitting packets at a time. Add in the neighbors all trying to use the radio band, and now you're competing with countless WiFi devices and a half-dozen or more WiFi access points. The result is usually less than desirable. Apartment complexes and condos are even worse than suburban single-family homes.
Observation #2:
Any new switches, routers or cables you buy should all be Gigabit, also called 1000Base-T. Some might mention a "hub", a device that's been obsolete for years. It's not the same as a switch which operates much more efficiently with much greater throughput. Ethernet patch cables to devices should be nothing less than Cat.5e, preferably Cat.6 (no plain Cat.5; I just purged a half-dozen from my SOHO). Your priority right now is the gigabit switch - upgrade the rest as time and money permits. I'd be looking for a solution to replace the Ethernet powerline adapters next.
What models are the routers (the one you use for gateway, and the one you tried to "split") Can one of them be turned into an access point?.. and then you would extend the range by putting one nearer to you, with a cable back to the first. ... as far as the connection out of the wall, you can't "split" ethernet, and in most cases you can add a cheap switch without issue. – TG2 – 2016-09-16T20:19:07.730
"Now I want to hook up my PS4 to the internet and want to split the connection that is coming out of the wall." use a switch you don't want to use a splitter in a case like this. Difference between Ethernet splitter and switch
– Ramhound – 2016-09-16T20:25:33.113Possible duplicate of Can I use a ethernet splitter to connect a router to two devices?
– Ramhound – 2016-09-16T20:28:11.2671The router should have been able to act as a switch. Something must not have been configured right. Make sure you disabled DHCP on the router since they should be getting their IP from the wireless router. – topshot – 2016-09-16T20:50:08.253
You probably just misconfigured the old router. Did you leave its WAN port empty? Did you disable its DHCP server? – David Schwartz – 2016-09-16T21:03:13.497