Yes PC2 will have the ethernet interface that connects to the internet probably dynamically assigned. But PC2 will also have another ethernet interface ( else it would be impossible to have another network).
That "other" interface, how is that one configured ? It can very well be that somehow that IP has changed, thus rendering the connection between the 2 pc's useless.
Just give the IP / subnet of that interface and the IP/subnet of the interface on PC1 ( the one you wrote down ).
