Not if you're in an internal network where a device (such as a router or broadband modem) acts as a DHCP server. /release will release your current DHCP lease, and /renew makes it request a new one from the DHCP server, however it could end up giving you the same one you had before.
/flushdns has nothing to do with your IP, internal or external.
Just wondering, do both computers show an aol address, even though the IPs are different? Something like 172-64.ipt.aol.com?
I remember back when I ran a decently popular irc channel, aol IPs where pain in the ass because you couldn't ban someone on aol without banning all of aol. I think all they had to do was unplug their modem and plug it back in to get a different address.