Hello Marcin
There could be several things that are going on here. Initially, you are able to access the DHCP server (since the laptop obtains an IP address) and the WLC from the laptop since they are on the same subnet and same VLAN.
Now when you introduce new VLANs, you must ensure that each VLAN has its own IP addressing space, that is, a defined subnet, and that the DHCP server is providing IP addressing information for all of these subnets. You must also ensure that the devices you want on the management VLAN (laptop and WLC) are indeed on the same VLAN, and those using DHCP (the laptop) are able to reach the DHCP server. Additionally, you have to make sure that these new VLANs are reaching the access points and that you have configured the appropriate SSIDs that correspond to these VLANs (if you are applying multiple VLANs to the APs). Finally, if you want communication between hosts that exist on different VLANs and different subnets, you must ensure that routing is configured.
Let us know how you get along in your troubleshooting efforts!
I hope this has been helpful!
Laz