I can only connect to one with RSLinx. The three I can't have the yellow question mark and red X over them.
The red X indicates that RSLinx cannot make a CIP connection to the controller, while the yellow question mark indicates that RSLinx does not recognize the device's identity.
EDS registries might still be an issue, but they're not the only issue. You need to resolve the red X first.
PING is handy, but it's a blunt instrument because it doesn't use the same network features that the rest of your software uses.
I would start by entering the IP address of each controller into a Web Browser. The built-in Web pages will let you examine how many connections each controller is using at this time.
While it's certainly possible to run out of CIP connections on the CompactLogix, your basic network description should not do so. The 1769-L35E supports 32 CIP connections, and a single PanelView can use up a maximum of 5.
What else is on this network that might be accessing those controllers ? Are you running some other HMI, or a bunch of RSLinx Classic browsing stations, or a bunch of messaging to other controllers ?
The connection list on the embedded Web page is really going to be your best place to start troubleshooting.