Any application that gives you web-based control of the desktop PC should allow you to exercise control of the devices connected to it. A good example is a program called VNC (Virtual Network Connection). Here’s a link:
If your OS is new enough, you can even do remote desktop with Windows.
As a side note, there are devices that let you connect more RS-232 devices through a single USB port. I’ve got a couple in service right now, that let me connect 8 serial devices each. RS-232 is still out there…