No you can't get around it unfortunately, your pc has to be switched on for your son to access the web as your pc is the host connection.
If your son wants unlimited web access without having to leave your pc on then you need to consider a different hardware setup.
Consider a wireless setup, they just as cheap as wired nowadays.
To set up the pc's so they have independant access you will need a router and two network cards for each machine.
A lot of the time people find they're limited to the type of router they can buy due to the way their modem connects, you have both options, usb and if you remove the act/link (blue box) you have ethernet.
An 802.11g belkin wireless router from ebuyer will cost you £41, add to that approx £30 for two wireless adaptors for each pc, offset that cost against a wired one and there isn't a whole lot in it £20-£30 at most. Then again you already have two network cards and a cable, so i'll stop prattling on and let you decide. :-)