Can I connect to my network in safe mode with networking?

Safe mode with networking starts the minimum number of services to necessary enable basic networking over a LAN or cable connection, but no more. If you are connected directly to the Internet, you will not be able to connect if your connection requires additional protocol support, such as the PPP (dial-up connections) or PPPoE (DSL) protocols. There is also no support for wireless connections in safe mode with networking. Note that if you connect over a router, the router has to handle any protocols the Internet connection requires, leaving you with a simple LAN connection to your router, so if you are connected via a LAN cable to a router, you can almost certainly establish a connection no matter what protocols are involved on the WAN side of the router, with the exception of tunneling protocols such as VPN. Note that there are routers that support even VPN.

In summation, you can probably connect to the network in safe mode with networking if you

have a cable connection,
connect via another computer using network sharing,
have a DSL connection that does not use PPPoE,
or have a DSL connection that does use the PPPoE protocol, but are behind a router.

You cannot establish establish connectivity if you

use a dial-up or PPP connection,
have a DSL connection that uses PPPoE,
have a satellite connection,
or have a wireless connection.

If you still are not sure, just try safe mode with networking and see if you can connect. This is always the surest way to find out.

See How to reboot to safe mode for instructions on how to boot to safe mode and safe mode with networking.