As mentioned in Part 1, you should move electronics between your router and computer so that it won't cause interference. This next part will require that you get into your router's settings and adjust them.
Look for labels on your router, you'll need to find the brand and its model. Next, you'll need to enter these numbers into your browser's address bar. If one of them doesn't work, go down the list:
192.168.1.1
198.168.2.1
192.168.0.1

Next, you'll need to do your own research on login information for your router. I have a small list below but in the event that it doesn't work for you, use Google.
Format: Username/Password(blank = nothing)
root/admin
root/root
admin/blank
root/blank
admin/admin
admin/password
user/blank


After logging in, you'll need to dig around your router's configuration. You'll need to change your Wireless Channel, I have mine on 11 but it may not be ideal for you. You can only set the channels from 1 to 11 however and you'll need to go through trial and error to test which works best for you. Channel 9 works for some people though so you might want to try that one.

I believe your computer is setting priority on your neighbor's router over yours. If you're fine with using teamviewer, I can help.

Teamviewer is a program where I'm able to control your computer while you sit back and watch. It's quite a slow and painful process if your internet connection isn't that good but I'm able to fix problems for you without any interaction.
Download: http://www.teamviewer.com/en/index.aspx

Good post. 1, 8 & 9, I need to correct.

Hope I remember in the morning. I'm tired. I need some sleep.
Sides, stupid winter storm coming our way