James, usually the shared network trick works flawlessly, so that might be a bug in the way it works. It usually sets up a special program called 'dnsmasq' on the shared ethernet device which should give your server a dynamic IP during the installation.
You may be able to work around this problem by simply giving your server a static IP address on the shared network. Open a terminal on the laptop and run
ip addr show
You should get a list with entries like this:
3: eth1: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP qlen 1000
link/ether 00:23:6c:87:2c:2d brd ff:ff:ff:ff:ff:ff
inet 192.168.1.105/24 brd 192.168.1.255 scope global eth1
inet6 fe80::223:6cff:fe87:2c2d/64 scope link
valid_lft forever preferred_lft forever
Find the interface that is your shared ethernet connection, and note the network, so in my case above:
My network is 192.168.1.0/24 and my address is 192.168.1.105
Pick an address (how about 192.168.1.2 in this case) in the same network, and assign it to your server. Give it your machine's address as the gateway and DNS server.
That should work to at least get the server able to transfer files from the internet. However, you still won't be able to use the server from any of your other computers because it will basically be firewalled behind your laptop. You can use "DNAT" rules to enable that, but that sounds a lot more complicated than just saving up for a wifi card. :)