Hi dvistaexpson,
The following provides driver downloads, software (I believe you need both - not just the drivers) as well as manuals, documentation, troubleshooting guides, and other help in setting up the printer. I suspect either you did not install both software and drivers on both machines or perhaps used the wrong versions (most likely on the server since that's the one indicating it has the wrong drivers installed). Since it works when connected to the 32-bit laptop, that suggests the laptop is fine, has the correct drivers, and also suggests that the printer itself is fine. I know you get an error if you connect the printer to the 64-bit machine and try to print from the laptop. Does the printer work if connected to the 64-bit machine and you try to print from that machine - in effect, does it ever work if connected to the 64-bit machine?
Download the manuals, drivers, software, and guides and follow the setup instructions step-by-step.
Epson Stylus Photo RX500, Overview - Technical Support - Epson America, Inc.. Although this does not have the (M), I could find nothing that included that distinction - so I believe this is what you need. Is this a US printer or was it obtained in another country (if so, where)? If the above and below don't help, then this page also includes a way to contact epson for technical support and that would be my next recommendation.
Some printers provide the option on the host computer to install additional drivers to support other computers that will be using it. Please check if that's the case with this printer and, if so, add the 32-bit Vista driver as per the instructions. That's what sounds like the case to me, but I'm far from certain as I lack too much information about the situation and the setup.
How did you setup the connection on the laptop to the printer when it is attached to the 64-bit system? Have you checked the printer setup on the laptop to verify what drivers it is using and that it is using 32-bit drivers and not trying to use 64-bit drivers? The difference may be in the setup procedures or even the networking setup - it's hard to tell without knowing exactly what you did and knowing exactly what was required for this printer (as I did not download or read the manuals myself). Sometimes having the printer on or off while installing the software and/or drivers can be enough to make the printer function or cause problems - that's why following the instructions is so important.
I hope this helps.
Good luck!