There is a task of optimum adjustment of job mail-server (about 30 mailboxes), web-server and internet access routing for office.
Our firm has two IP-address from two different providers.

The first provides access for the speed 128 кбит/с on technology xDSL but with faults of connection. This address uses the Server (a Pentium 4, 512Mb) under RedHat Linux9 on which such services are placed: DNS-server, mail-server, web-server, web-site+postgresql.
The second gives access for the speed 256 кбит/с by radio without essential faults. This address uses Router (Celeron, 128Mb) under RedHat Linux9 and carries out functions of routing of Internet - access for office.

I want to commission Newserver (a Pentium 4) under ASPLinux and to start on him DNS, mail-server and NAT-routing instead of Router that mail could work trouble-free. But I want to leave on the Server a web-site because to copy it on other machine and recompile there is problematic.

Whether it is possible to make so that DNS and mail worked on Newserver, and the Server remained in the domain mycompany.com and site was accessible as well as earlier to the address www.mycompany.com? If yes, as it to make?