The modem you have is ZyXEL from PLDT?
Bro May I know what is the IP address that your getting from the modem when u directly connected to it?? is it private IP or public IP?? or anyway can you post the IP here..
As far as I know, most of the DSL ISP provides Modem/Router.. if ur ISP set the modem to full-bridge mode then you should have a username and password given by your ISP for the authentication of the connection. If your modem is set to Automatic Configuration - DHCP (Half-bridge mode) then there is no need for username and password for authentication and normally you will be getting a private IP from the modem. ISP will use the MAC address of your computer authenticate the connection.
PLDT will only allow 1 computer to gain internet access. thats why you should get a router for multiple computers to gain internet access..
your setup is Modem/Router - Switch - multiple computers
still with this setup only 1 computer will be able to get internet access because the switch is not a DHCP device and your modem/router will only provide one IP as set by your ISP
since you have a wireless router then why don't you setup the network like this
Modem - wireless router - switch - multiple computers and this fix your problem
UPDATE:
I Just tried the same setup with yours
Modem/Router - switch - 4 computers
2 computers is able to get online but its sharing the internet (kung ang isa kay ga youtube ang isa ka computer kay hinay kaau internet) sharing the internet connection. the other 2 computers unable to get online at all..
Anyway my setup here at home is
Modem/Router (ZyXEL from PLDT) - Wireless Router - 8 port switch - 3 wired computers and multiple wireless device (laptops, wifi phones) and no problem with the internet connection at all.
Edit:
you mentioned above the IP which is 112.202.X.X
is that the IP from the modem?? in that case your getting a public IP address..
Fix your problem with this setup then..
MODEM - Wireless Router - Switch - computers