In Firefox when you click Tools > Add Ons > Plug Ins
Then click on the ArcadeOX plugin it should show a button to "disable" it. If it has a button that says "enable" then that means it is disabled and you need to click the enable button. If it says "disable" then you should be good to go.
From what you have described it sounds like it should be working. Is there any weird software on your computer? Are you at a work or library or school that might have a firewall that blocks certain sites?
Can you download this file
http://www.third.arcadeox.com/g/colecovision/tapper.zip
How much free space do you have on your C drive?
The Windows Key has a flag on it and is to the left of your space bar. Press the Windows Key + R. That opens a run prompt. In the run prompt copy and paste this
%temp%\low\arcadeox
then press enter.
Does that open up a folder. Are there files in that folder?