Norton will not open, and neither will Internet Explorer

So, over the past few days, there has been issues with my grandparent's laptop.. It's been freezing and locking up while they use it (Though I have been on it with no issues at all.), and today, we cannot get Norton to open, nor Internet Explorer. The computer did an update last night, however, as did the one I am currently using. The one I am currently using works perfectly, including Norton and I.E.. But my grandparents' computer is not. They are both Windows 7 HP Laptops.

Here is what my grandparents' laptop is doing today: Norton will not open, at all. There is no error message when we try opening it, or any pop ups or anything. It simply does not open. I've tried running it as Administrator, tried Troubleshooting it (after which it says one of Norton's files are incompatible, when it was working yesterday, and even when it says it's fixed, it isn't), tried opening it several different ways, and none of them work. At all. I'm worried that the computer has somehow obtained a virus, and that it's preventing Norton from opening.

And while we are having this issue, Internet Explorer will not open either. (Big surprise, I.E sucks, but it's the only browser they will use, so this needs to be fixed.) It attempts to open - you see the clear outline of the browser flash onto the screen for a split second, before it suddenly closes itself as fast as it opened. If you blink, you'd literally miss it. And like with Norton, there's no error message. 

I've restarted the computer several times, as well, and they still do not work. everything else on the computer - Games(both my grandma's and mine), Google Chrome, Skype, Steam, GIMP; They all work. It's just Norton and I.E that are refusing to open.

Can anyone help me fix this? I'm the only one in the house with any technical know-how, and I'm being blamed for the two programs not working, despite that and the fact I'm always the one to fix our third computer when my grandmother downloads viruses trying to print maps off the internet.