laevanay,
You have defined a zone, but have you set that as Trusted (using Security/Tasks) so that it creates two rules at the top of Network Monitor? If these two rules are not present, the zone is not being applied. You should have in position Rule ID 0 this rule: Allow IP Out from Any to Zone where IP Detail is Any. In position Rule ID 1 you should have Allow IP In from Zone to Any where IP Detail is Any.
If those two rules are in place, have you rebooted since you did so? If not, please do.
If it's still not working, temporarily set CFP Security Level to Allow All for testing purposes only. Try to access your LAN. If it fails, it is not CFP blocking you. In that case it will probably be the residual traces of your previous firewall causing a conflict.
If Allow All enables your LAN connection, then CFP is blocking something somehow. The Logs will hold the clues. Open Activity/Logs, right-click any entry and select "Clear all logs." Then try to access your LAN (with Security Level returned to Custom), with no other programs running. Once it fails, go back to the logs, and look at the very bottom entry (as this will be the oldest); that is where we will need to start.
LM