Hi Kyle,
Do you mean that the mapped network drives that connect to SharePoint Online sites on your computer won’t work again after the IE upgraded to IE 10?
To resolve the problem, please disconnect the network drive and re-connect it again referring to the steps below:
1. Sign in to the SharePoint Online site by using your Office 365 credentials. Make sure that you click to select the Keep me signed in check box.
2. Right-click Computer, and then click Map Network Drive.
3. Click the Connect to a Web site that you can store your documents and pictures link, and then click Next two times.
4. Type the site URL, click Next, and then follow the instructions in the wizard. For example, type https://contoso.sharepoint.com.
In addition, you can refer to the following article to troubleshoot problems when using mapped network drives:
support.microsoft.com/.../2616712
Since I noticed that the problem you met is different with James above, if the issue persists or anything unclear to you, it will be better if you can post a new question in the forum, so we can help you more efficiently with your situation.
Thanks,
Nancy Xie