First off, I am very surprised that they all connect and speak to the default gateway. The way your subnet mask is set, you should only have 8 IPs on your network, that's including the gateway. The range that the machine you showed the configuration for should be able to speak to, is: 10.32.11.40-10.32.11.47. However, with this configuration, .40 is the network address, and .47 is the broadcast address, that leaves you with 6 hosts, one of which is the default gateway, .41, this leaves you with only room for 5 hosts to communicate. Your modem is giving out the IP addresses, which means it's information is 10.32.11.41, with a subnet mask of 255.255.255.248. Somehow you are getting lucky by this not causing a conflict of IP address assignment.
To fix:
Cross our fingers that we can reconfigure the address that your modem is using, and the addresses it is giving out. (DHCP) I'm not sure what model your modem is or the features it carries. You may have information as to how to access the configuration in the modem that your ISP could have possibly given you. If you have no access to the Modem, I recommend the second option.
OR
You purchase a small router, doesn't need to be anything fancy, and insert it between the modem and the switches. I would recommend a simple router. The ports it would need is a WAN port, and AT LEAST 2 switch ports, if it has more that's fine but the UPLINK port(if any) doesn't count for a switch port.
What we are trying to accomplish, is to establish a network that can have all of your hosts connected at once. If all of them are able to connect to the internet at one time as is, I am very surprised, and do not see how that is possible. The IP scheme that you are using internally is too small for 8 computers. If we can change the subnet mask in the modem, we may have a shot at not spending anything.
The thing is, by using only the switches, we can set up the internal network to do what you want, but there would be no internet.
Greazy Mcgeezy