Hello myheadhurt, I have outlined a few of the mistakes which hopefully will help you set up your static IP's.
PC1
1. Just right-click “My Computer” and click Properties.
2. Select the “Computer Name” tab and click the “Change” button.
3. Change the computer name to whatever you want, here we name it PC1. Change the workgroup to WG. (The workgroup name should be the same in both computers)
4. Click OK.
Now, to configure the TCP/IP connection settings,
1. Goto “Control Panel” >> “Network connections”
2. Right-click on your LAN connection and click “Properties”. In the “General” tab, select “Internet Protocol (TCP/IP)”. Click the “Properties” button.
3. Set the Values
IP Address – 192.168.0.1 < You are using the default gateway as your IP address here which is incorrect.
Subnet Mask – 255.255.255.0
Default Gateway – 192.168.0.2 <This isn't correct, the default gateway needs to be the same on both machines and should be 192.168.0.1
4. Click OK and you are done for PC1.
PC2
Now, to configure the TCP/IP connection settings,
1. Goto “Control Panel” >> “Network connections”
2. Right-click on your LAN connection and click “Properties”. In the “General” tab, select “Internet Protocol (TCP/IP)”. Click the “Properties” button.
3. Set the Values
IP Address – 192.168.0.2 < this is incorrect, both PC's need a different IP in the proper range, usually starts at 192.168.0.100>199 range.
Subnet Mask – 255.255.255.0
Default Gateway – 192.168.0.1 <This is the correct default gateway, this needs to be the same for both machines.
4. Click OK and you are done for PC2 as well.
And as Docbrown mentioned you will want to set up a Workgroup for this network.