Dread, there have been numerous posts concerning this recently. Depending on the PLC involved, the USB/serial may or may not work. In my case for Allen Bradley I could do DF1 but not use a 1747-PIC. I didnt have problems with GE Fanuc (that surprised a GE Fanuc tech), or automationdirect. For Allen Bradley and Siemens I had to obtain the PCMCIA card, still have issues with Siemens in XP tho.
All in all I keep my personal laptop (IBM 300mhz with Win98) close by with all software etc loaded on it.
May want to check with Omron to see if they have an update to your Omron software to work with your OS, I assume the new laptop has Win2K or XP on it.
Another option (research this thoroughly) if you have Win2k/XP and the software wont work with either is to dual boot. The easiest way to do this is get Partition Magic to create another partition then install Win9x. I state research this thorougly because some of the newer laptops (especially XP systems) may not have the system/device drivers available for Win9x.