192.168.0.x or 192.168.1.x are IP addresses 255.255.255.x are the subnets. It would'nt help to get them confused.
In all else oneman is correct and now that we know you have no router that might narrow it down a bit.
Have you installed the modem and any drivers it requires on the lappy properly?
Is your firewall set to allow the connection?
255.255.255.0 is a subnet mask
255.255.255.x would generally indicate a subnet mask in the range 255.255.255.0 to 255.255.255.254
192.168.0.x is a generally used to indicate a subnet with mask 255.255.255.0 though technically it should be written as 192.168.0.0/24 in MS speak but that really is confusing.
Anyway,
There used to be two ways to connect the modem, either USB or Ethernet. I don't know if USB is supported these days, the last few cable modems have been ethernet only.
If the modem is USB then yes you will need modem drivers. But then I think the modem shows up as a dial-up device not a network device (this is years ago, back in 96 or 97 that I had a USB modem so I could well be wrong).
If the connection to the router is Ethernet then no drivers should be required for the modem, only for the ethernet card and from the laptop ipconfig looks like the drivers are installed.
Also back in the dark distance back, blueyonder and NTL used to lock down the connection by MAC address so you have to register which computer was connected to the modem. So if you switched between laptop and desktop you would need to call them. Again I think they dropped that years ago.
pops1a any change you can take your laptop to a friends or neighbours house and plug it in there. It will at show your ethernet port and drivers are working.
Also have you called virgin, there may be a simple solution to this.