Hi Sarah,
Thank you for all the great information! I find it strange you can't access systemcontrolcenter.com and the messages are telling you the default gateway is not available. This is going to be a very long post, but I would like you to test your internet connection after every step.
1. Check your internet settings
Start > Control Panel > Network and Internet > Internet Options > Connections Tab > LAN Settings
Once in LAN Settings, please ensure that the only box that is checked is "Automatically Detect Settings"
Click OK
2. Check your adapter settings
Start > Control Panel > Network and Internet > Network and Sharing Center > Change Adapter Settings // Right click on Local Area Connection and select "Properties"
The properties box will appear. Select Internet Protocol Version 4 and click on the Properties button. Ensure both the circles for Obtain IP/DNS address automatically are selected. Click OK
3. Reset your network settings
Click start and open your Command Prompt by right clicking the Command Prompt and selecting "Run as Administrator". You can also search from the search bar after clicking Start and typing CMD in the search box.

Type in the following line and hit enter: netsh winsock reset
You will need to restart your computer.
There are a lot more things we can do, but if we have to do more than 3 steps I would rather you speak with a technician here in our office. Let me know if any of these steps get you working.
Thanks,
Amanda