the pix doesn't care if its public, private or other wise, you need to make sure that you have the appropriate routing and nat statements.
When you say it doesn't work, what do you mean, do you see any errors in your "Debug crypto iskamp" or debug crypto ipsec sa
Also, im assuming that the private address that worked was (inside) and the new tunnel your creating is from (dmz)
make sure you have nonat configured for traffic from (dmz) to remote (inside)
on the remote side, make sure you have routes pointing your (dmz) public addressing out the interface that facilitates the vpn tunnel to head office.
we would need more infomation like configs and/or diagrams to help further.
remmeber the check the nonat/nat statements on both ends..
