[SOLVED] Ethernet and phone cables mixed?

Solution
The cable will probably support ethernet but you will probably have to change both ends of the cable. The ends in the rooms are probably wired just as poorly.

In the cabinet you show, you can put a patch panel and then jumpers to a switch.
The cable will probably support ethernet but you will probably have to change both ends of the cable. The ends in the rooms are probably wired just as poorly.

In the cabinet you show, you can put a patch panel and then jumpers to a switch.
 
Solution
They look like ethernet look at the markings on them.

You should be able to replace the phone patch panel with a data patch panel. Depending what is on the other end you likely will have to replace the rj11 keystone with rj45.

Not sure why they still put phone jacks in it is kinda rare to have a land line anymore and if you really want to you can just plug rj11 cables into rj45 jacks, they fit a bit loose but work.
 
You still need to buy an ethernet patch panel and a network switch to put in that cabinet.

What's on the other end of those cables? Are there ethernet port on some of the walls of your house? If so, you may need to take the wall plate off to look behind it and see how it's wired, as either 568A or 568B. Then you much match that wiring on the panel box end.