Along the lines of what Samrae helpfully suggested, I opted for a virtual private server, with the main difference apparently being that I can then run apps with an Internet connection even when my PC is shut down.
I've installed Macro Express, a browser, and a Notepad page with URLs to be copied in a VPS running Windows Server 8.
The issue now is that Macros captured there do not function when run. I tried both mouse-click capture and keystroke capture. When played back, the cursor just moves around a little on the Macro Express window.
If someone can now suggest a solution for this issue, I will be getting somewhere.
Thanks in advance.
NOTE: I am still using the mouse and keyboard installed on my PC. I am not clear on whether some adjustment is needed there.