Oh ya I apologize.

1. Hit your windows key + R
2. type 'cmd ' press enter
3. follow with my original post

This doesn't work if you are at an organization with certain firewalls, such as on...

You can use the ping utility in windows.

1. Bring up command prompt
2. Type - ping www.google.com
3. replace google with whatever website you want

I can't answer your modem question, but have you considered setting up an Ad Hoc network?

http://www.cs.washington.edu/research/edtech/presenter/doc/adhoc.html

Should let you share your Verizon...

Yes, any computer that you want to access has to be turned on in order to access it. Was that your question?