Can anybody hack without using Trojans?

Hi all..

Can a hacker hack a PC without putting a Trojan in it?

And if that PC2 is connected to a LAN and the main PC1 is connected to the internet. So can the hacker put a Trojan using a port opened? And if that port is in use.. then can he do that? (All ports are closed)

And how to protect that? What is the best solution?

Notice : I want only the main PC1 to transfer data to PC2.. so if hacker got into the network.. then he can't do anything..

Important info and files are in PC2 that is not connected directly to the internet but connected to PC1 using a LAN..

Regards..