I took your advice.
Here's what I did.
I go onto the router by entering its IP into my browser address bar http://192.168.1.254
and accessed the control panel.
Then I turned off DHCP.
I then found IP passthrough, and I enabled "user configured pc"
I then went into the Mandrake control center and accessed networking, and I turned off DHCP there. I chose an IP address for my pc
I used this as subnet mask 255.255.255.0 (standard for most PC's I think)
and for a DNS server I used the modem address
And I rebooted.
eth0 detection took about 2 secs instead of fifteen seconds, and networking worked like a charm.
Strangely enough, I had a more difficult time configuring my Windows XP to operate using the fixed IP - the jargon in the M$ dialog windows is annoyingly inaccurate and so user friendly that someone with actual knowledge has trouble navigating. But I did it ok, restarted, and everyone can access the net and both operating systems boot more quickly.