I think its because u have configured the port towards router as an access port.Try with making it a trunk port on both 3560 and router side or make it an L3 port using "no switchport" command on 3560,gave both ports an ip and then put the default routes next-hop as the ip on router side.
I think your problem may not be in the configurations of the switches at all, but in the clients. Do I understand that your hosts connected to the 3560 can connect and the hosts connected to the 2960 cannot?
The 2960 is a layer-2 switch and will not do routing at all. So ... what default gateway have you configured in the host clients? If it is the addresses on the 2960, hen it will not work at all. The clients need to use the IP addresses of the 3560 as their gateway.
I just had another look at your configurations. In you 3560, you have a static default route via 184.108.40.206, but I am not sure you have a route to 220.127.116.11. I suppose it is out the F0/1 port, but the 3560 does not know that.
You need to configure something like this on the 3560:
ip address 18.104.22.168 255.255.255.224
Then, make sure you can ping 22.214.171.124 from the 3560, and check that your default route has turned up in your routing table.
The ISP router will know about 192.168.101.0/24 because of it secondary address presence in the VLAN 101 (although you will need to resolve its IP address conflict with the VLAN 101 interface of the 2960). But the ISP router will need to be told about 192.168.102.0/24 and 192.168.103.0/24. Does it run any routing protocol? If so, and once it know about 192.168.102.0/24 etc., you could handle 192.168.101.0/24 in the same way.
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...