This is an interesting problem because a printer isn't "intelligent" the way a computer is "intelligent". While devices such as the 6110 have RAM and thus "memory", they don't have the ability to recognize which devices are connected to it, as such. That's why you have to install all of the HP software and drivers onto the Windows or Mac machines, so the burden of recognition and interfacing is on them.
That said, information and even errors can be stored in a printer as long as it's receiving power...sometimes even when they're turned off.
My first suggestion is to completely turn off the 6110 and unplug it both from it's supply of power and from any computers.
Let it set for around 30 seconds to a minute so that any residual power from the "brick" dissipates.
Reboot the Windows computer.
Then plug the 6110 back into it's power supply and attach it back to the Windows computer.
Power up the 6110 and let it go through it's start up and alignment routine.
Try to scan again as you originally did before you tried to us your Macbook with the 6110. Hopefully that will do it.
If, for some reason, the Windows machine is still not able to interface with the 6110, you may have to completely uninstall all of the HP software and drivers from the laptop and reinstall them using the original installation CD, just as if you were installing the printer with the laptop for the first time.
This means (assuming you have Windows XP), going to Start -> Control Panel -> Add or Remove Programs. You'll need to go through the list after "Add or Remove Programs" opens to select and uninstall all the software and drivers that have anything to do with the 6110. Hopefully, this'll be just one or two selections.
If you have the original CD, you can also insert it and it should offer you the option to uninstall the original software and drivers. That would be the easiest. Then you could just turn around and do a reinstall from the disc, no muss, no fuss.
If you do not have the original CD (and believe me, these things get lost all the time), you can still download all the latest software for the 6110 onto the Windows laptop by going to this web page at HP.com:
Officejet 6110 Software and Drivers
Once you go to that page, you'll need to select your particular Windows operating system name. You'll be taken to the web page where you can download the installation software and the latest drivers. Once they're reinstalled onto your system, you should be good to go.
You "may" be able to install the latest software and drivers without uninstallng the old stuff first (that is, you could be offered the option to overwrite the old software when you install the newer software),. but that's not as "clean" and instead of curing the problem, it could make it worse. If you're a risk taker, go for it. If not, don't take the chance of more headaches.
I probably made this sound more complicated than it is. Good luck and post back your results.