The cable is not likely the problem at all (most modern devices designed for SOHO use, anyway, do auto-detection of cable type), unless we're using old or highly specialized or pricey equipment, BION (and I'm ready to be proven wrong on that).
You're either going to have to set up some specialized route tables, or else you're going to need to reroute the cable, as best as I can tell. Note that I'm assuming these boxes aren't smart enough to do what you're asking them to do. I'm not a real net guru, so it's possible that someone with a little more knowledge of routing could make it work just the way you have drawn it.
The problem: I can't say for sure, but in looking at your diagram, I'm guessing that the "wired router with 4 devices attached" is having trouble grokking the setup, because it expects that any traffic coming from the "4 devices" is LAN traffic and should all be routed to the 4 ports on that side only. A quick fix would be to only run 3 devices on that side, and take the cable from the "combined wireless router/modem with one LAN port" and put it into the remaining LAN side port on the "wired router".
Then, your only problem will be getting the correct GW addy on the 3 wired boxes. If this works and the GW is the only problem, I'd just have the wireless router do all the DHCP work (IOW, shut off DHCP on the wired box, effectively just using it as a hub [which is pretty much what I'm suggesting anyhow]).
OTOH, like I said, it might be possible to have the wired box route this correctly, but I'm not enough of a routing guru to fix the problem (only tell what the problem is likely to be) without sitting there and playing around with it.
HTH,
