A Reset has the side effect of stripping away some of your extensions. You can review and disable extensions right now on the Add-ons page. Either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable anything nonessential or unrecognized.

Usually a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that shut down the ads?

You might also want to use some of the malware scanning and cleaning tools listed in this support article: Troubleshoot Firefox issues caused by malware

If this can happen with Firefox completely closed:

Some malware simply launches pages in your default browser from outside Firefox. Definitely scan for malware using some of the tools listed in our support article: Troubleshoot Firefox issues caused by malware.

There might be an additional step:

Last year, many users reported advertising tabs opening randomly, sometimes even when Firefox was closed. It turned out that a program had created scheduled tasks to open those pages at certain times of day.

You can check the Windows Task Scheduler:

• Windows XP: Start button > [All] Programs > Accessories> System Tools > Scheduled Tasks

• Windows Vista/7: Start button > Control Panel > System and Security > Administrative Tools > Task Scheduler

• Windows 8: ?? You might try the charms bar search box if you don't find it in the control panel.

• Past threads on the "dsite" problem:
  • How can I keep Firefox from opening a window to website tofushopnews.com
  • How do I get rid of sponsorship tabs that open automatically?