Cabling the office, router and switch are 1GB, same for ethernet ports on computer but speed is 100-200 at best

I have got a new office,(one room dedicated to servers, 4 rooms for employees. I have got 1 switch for each room, with 4 Gb ports each, and one router with 4 GB ports, which act as both wifi router and LAN, connected to a cable modem.

The issue is that I am getting pretty low speed all over the network. The person that sold me the place, told me that they cabled the office with Cat6 cables few years ago; although they are in the wall, so I have no way to check them.

Is there an easy way to verify the speed of each element on the network, to figure out if the problem is the cables in the wall? I am using the wall cabling from the modem to the router, and from the router to the wall plugs, which connect to the switches; I checked the cables that are not in the wall, and they are CAT6, so should support gigabit ethernet like the rest of the hardware.