looking at you network design sketch, I can say your network is set up completely wrong.
First, what type - brand - model is the switch that you have the DSL modem plugged into?
Unless that switch also does the type of routing necessary to manage your WAN connection, you definitely should NOT have the modem plugged into it. Switches are not routers, Routers are not Switches. They each server different needs in a network.
Another issue i see right away is that you should never connect the WAN port of your router to a switch port on the same unit. Most manufacturers use this to do a hard reset of the equipment, it also creates a loop in the equipment. Simply BAD network design.
Take the advice of others who posted the same suggestions.
connect your ISP equipment to the WAN port of your linksys router.
If you don't want LMCE doing dhcp, then you can set the linksys router to hand out ips and turn it off in the LMCE admin pages. But you really do need a router/gateway device managing the WAN interface. A switch is simply not designed to do that.