Having trouble installing Brother MFC-J470DW printer.

  I called Brother Support and after two hours of trying everything they could think of, the tech told me that I should call Microsoft as the problem had to be with them.  When I start the install disk it goes only so far and then it stops.  Gets as far as "plug in cable" and turn your machine on.  And then it just sits there doing nothing.  I've tried system recovery and it didn't help.  How do I go about getting this problem fixed?  

It sounds like a brother problem or one you aren't going to fix in a forum such as this easily and the first bit of advice you are going to get:

Restore the machine to factory defaults (likely an OEM, not Microsoft, method) after backing up your important data and collecting your installation media and product keys/serial numbers together.  Then install latest hardware device drivers and all Microsoft updates including the printer after you have restored to factory defaults (likely an OEM, not Microsoft, method.)  Then install all of the other stuff.

Why that advice here?  If the people who made and support the device (the only one you are reporting having issue with) could not fix things - and you have given NO DETAIL on what they had you try - you could waste time here discussing all of the same things over again without the expertise of those who intimately know their own device, wrote the software you are trying to install and tested it on the operating system you are trying to install it on - or you could start everything from a CLEAN and KNOWN GOOD state and if it fails then - be able to troubleshoot with those at Brother or just return the product as a dud.

Now - if you really think that sounds like a pain - provide some details about what has and has not been tried, etc.

Other suggestions:

If you are using this:

Full Driver & Software Package

... as your starting point (that is for your device), let's simplify and get the printer installed first.

Download just the driver (Assuming Windows 7 64-bit, another bit of information to provide):Printer Driver & Scanner Driver for Local Connection

... decompress it, go to the folder where you decompressed it so you can find the full path and..

1. Open Devices and Printers by clicking the Start button , and then, on the Start menu, clicking Devices and Printers.
2. Click Add a printer.
3. In the Add Printer wizard, click Add a local printer.
4. On the Choose a printer port page, make sure that the Use an existing port button and the recommended printer port are selected, and then click Next.
5. On the Install the printer driver page, select the printer manufacturer and model, and then click Next.
   • Click Have Disk, and then browse to the folder where the printer driver is located (see above).
6. Complete the additional steps in the wizard, and then click Finish.

Did it add a printer to your list of Printers?  Can you print?

Also, in all of their troubleshooting, did they have you save the Full Driver & Software Package and right-click on it and Run as Administrator?