This is part of your problem. If you are using SSL to connect (https instead of http) you need to open port 443. SSL doesn't work on port 80.
And you might try this re-write of your rule:
iptables -A INPUT -s 192.168.0.0/24 -i eth0 -p all --dport 443 -j ACCEPT
The 192.168.0.0/24 will allow any IP address from the 192.168.0 range so if you are using DHCP for your internal network, you don't have to worry about setting up static IP addresses. I'm also a little confused about why you want to limit the source port range. This actually may be another part of the problem unless you know that your browser is always going to use those ports. Unless yo've done something to lock your browser down, odds are it is using something else. Finally, unless you are using this box as a router, -i eth0 and -d 192.168.0.2 are kind of redundant. Personally I prefer to use -i, but that is a personal preference.