If you can ping other computers and other computers can't ping your computer, this is often caused by an improperly configured firewall
on you computer. For example, ICF should not be enabled on LAN NIC.
Q: Can I setup two IPs that belong to different subnets?
A: Yes, but you must use static IPs instead of DHCP and they must be in the same subnet. To do this, open the Properties of TCP/IP>Advanced, click Add to add IP addresses.