Networked PCs - continuous dial-up

I have recently purchased a new PC and have networked it to my old PC, using a cable. I use dial-up to connect to the internet. Everytime I switch both PCs on my old PC connects to the internet and the only way I can stop it doing so is to physically break the network (i.e. disconnect the cable). At present I can't network both PCs without being on the Internet.
How do I solve this problem?

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