Dear Junior Admin,
I applaud your efforts, to get the some of the workstation to pick up new leases from the new DHCP scope. You may have missed a few steps though. You see when the PC comes online, does a broadcast looking for a DHCP server. DHCP server responds with an OFFER message, offering the PC an IP address, subnet mask, and default gateway, as well as various DNS options, and WINS if configured.
The PC sends back a DHCP ACK message, then the DHCP server sends back an ACK, letting the PC know the IP address has been reserved for the leas e period. At this time the PC will not contact the DHCP server again until halfway through the lease time. Default lease time is 8 days. If your PCs renewed their lease on Friday, they will not renew their lease after Scope is reconfigured until a default of 4 days from their lease renewal. Maybe longer, depending on what their original lease was configured for.
So, to force all the PCs to grab new IP addresses, you need to go to each computer, open a DOS prompt, and do an "ipconfig /release" and an "ipconfig /renew". If this does not work, you need to check your scope configuration, and make sure the network/subnet mask match what is configured on the router that is connected to this a particular LAN. Also you might need to see whether your DHCP server is on the same LAN, or whether your organizational IT is doing DHCP relays, etc.