Word does see that there is a printer ready to use? Also you said windows 7 see's it as the defualt printer, does windows 7 still reconize that? If windows still see that the HP printer is still default then your problem may not be with Windows it's self but possible with Word. Have you printed a test page, if so and it printed then your problem is with word not printing rather then a problem with windows. Also if your just clicking on the "quick print" button and the computer glitch out and maybe the printer isn't set to default printer, it won't printer. Just double check that your printer is for sure your new HP printer. Then hit the following key combo "CTRL+P" this will bring up this will bring up your printing menu for Word, it will then by default select the default printer, if nothing is selected then you could try selecting the printer and try printing your document again. Also one thing that could have happened is that when your installed your new printer it may have created a conflict with word and you may need to do a repair install. You can do this by following the provided setups below:
1) going to control Panel
2) locating "Microsoft office"
3) click on it and hit change/modify
4) when the pop up gives you options select "Repair"
It will then repair your installation of Microsoft office, when it has finished i would recommened doing a system restart if it does not prompt you do do so. I hope this infomation has helped you out.