I've had a look at
the nbc video page and can not find any section that says anything like "download player", so am not at all sure what you were actually attempting to download.
Could it have been a flash player you needed to install to watch the content?
If so, this is a fairly generic component used in a lot of websites to embed videos..youtube and the like. It can be obtained
here. (NB, as part of the install routine, it is recommended for you to not included the McAfee scan. It is also required to download and install the appropriate version for your browser.)
System restore is a bad idea in this sort of circumstance, as it is not a true restore. Some files will not be restored. The registry entries (basically Windows commands on what to do with a particular set of files) will be restored. But not anything done since that restore point. It can be a good way to get Windows a bit confused.
I would recommend a full uninstall, using the Avast built-in uninstaller, then the
Avast uninstall utility, (see the instructions on that page) then install afresh from scratch.
You should obtain all the files you need for this before uninstalling Avast, so that you can be offline for that.
Go online again after it's all re-installed, and up and running, and get updates. Then maybe visit that adobe site to get the flash player. Do that in the browser you wish it to be installed to, or all browsers (IE as well) if you want.
Does that help? Any questions about procedure/reasoning, please ask.