Am I limited to how many players I can use for free? I have two running in my home but I can't get a third one to connect.
There is no limit to how many Roku devices you can have.
Your internet connection (speed) may determine how well they will all be able to operate at the same time, but there is no "limit".
What are the model numbers of your working Roku devices and the suspect/problem Roku device (Settings/System/About). Also, router model number and ISP (internet service provider). Any error messages on screen.
At one time, long ago, I could not get something or other to work and received an error saying something like I had exceeded the 20 device limit for my account. Of course I only had 3 or so devices at the time, so the error message itself was completely in error, but perhaps the 20 Roku limit/account may have some credence.
I have 3 Rokus linked to my account at the present time, and some folks have quite a few more. So there is probably something else going on with your 3rd Roku.
What are the model names and numbers of the two connected Rokus and the one unconnected one? Settings > System > About will show you.