OK, lets get some basics checked
Most routers are set up by default to hand out DHCP IP addresses in the 192.168.0.0/24 range. This is what seems to be happening for you, as you are getting the address 192.168.0.1 sometimes. You should be getting this address ALL OF THE TIME (if your router is switched on).
The 169.254.x.x address you are getting is an 'Auto-configuration' address, which is a kind of emergency fail-safe for when the DHCP server dies.
Note. I am assuming that your are connecting to the internet via a router.
Please do a ipconfig /all command (Go to Start->Run and type "cmd -k ipconfig /all" no quotes)
I suspect that where your IP address says 192.168.0.1, there will be a corresponding subnet mask of 255.255.255.0. this means that you will have to change your PS2's IP address to something like 192.168.0.2, which is on the same network. 192.168.1.1 is on a different network if the mask is 255.255.255.0
Do us a favour, run the command as shown above and then paste a copy of the IP address, subnet mask and default gateway (Do not do this if your ip address does not start 192.168 or 169.254, you might give away sensitive information)
Sorry for the horrid explanation, it's difficult to explain in writing, especially to someone who is not too familar with subnet masks and the like, but bear with me and I'm sure we can sort this out.