To completely remove OneCare, use the Cleanup tool - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=828910&SiteID=2
If you lost Internet connectivity after installing Windows Live OneCare, there may have been a conflict with other security software left on the PC before installing OneCare. I don't know what you mean by "important hardware things" as OneCare is on a single PC and the network connection is for that PC, through the router or modem to the Internet. External hardware connected to the router should not be affected unless you let OneCare configure wireless security and the devices you are referring to are connected wirelessly to the router. In that case, you would need to follow the instructions provided during the security configuration to update the security information on those devices for connectivity.
If you need help, please contact support.
How to reach support (FAQ) - http://forums.microsoft.com/WindowsOneCare/ShowPost.aspx?PostID=2421771&SiteID=2
-steve