How could the DHCP server on your linksys be inadequate? Does it not support 254 DHCP clients? (my linksys does)
Assuming you have more than 254 DHCP clients on your LAN...
I have never set one up, but...
You'd need an OS that supports a DHCP server like Windows Advanced Server 2003 or FreeBSD or Slackware for one.
If you do not replace the linksys with this server PC as your new gateway (the logical thing to do), disable the DHCP server on the linksys, then configure the new DHCP server with a static LAN IP address, tell it what your DNS server IPs are (and hope they do not change), tell it the address of the gateway, the desired netmask and give it a range of IP addresses to assign, et viola!
If it is a limitation of the wireless router, then I'd get a wired router for superior performance and greater configurability.
The other option is to skip DHCP altogether and configure your 254+ PCs statically (but that would be a lot of work and maintenance when your ISPs DNS servers change).