IF you have a static IP, you don't need to use DNS unless you want something nicer than an IP to enter.
Since you're behind a router (which I"m assuming is running NAT), you're going to need to port forward to a pc to get anything through. The downside of that is you can only forward the port to 1 pc.
For remote desktopping, I would just use windows remote desktop (mstsc.exe). It uses port 3389/TCP.
Then to access your pc, fire up remote desktop whever and enter your static IP for the computer.
For file access to the other pc's, just fire up FTP. You'll need your windows cd (this works on server 2003/2l and xp/2k). Go into add/remove programs. Choose windows components, and install IIS (make sure in details the box for FTP is checked).
Once this is done, you will be able to access your main pc via ftp://hostpcname
in ie or windows explorer. The default FTP directory is c:\inetpub\ftproot
If you want to configure that differently, poke around a bit or search the MS site for how-tos.