First even though the printer is on a NETWORK do not add it as a Network printer to your Windows 7 system.
The main problem will be running / installing 32 bit drivers
on an X-64 system which is a NO NO. So we do a "Poodlefake" operation which tells the computer to treat the remote printer as a LOCAL device -- that way we can use the 64 bit driver
on our LOCAL machine - your laptop.
The windows spool system will have got the data ready before finally sending it to the remote printer.
I've posted this type of stuff before -- but here again is the info on what to do.
what you do is the following
1) add new printer
2) Choose LOCAL Printer
3) find out the network name of the printer --for example \\dogsbody\junkprinter
4) click create a NEW Port in the add printer wizard from the control panel
5) select LOCAL port (unless your printer is a purely networked printer with an IP address then chose TCPIP port and enter the IP address -- usually however the Network name like I've specified in 3) will be sufficient
6) enter the network name as in 3 or ip address
Now you'll get prompted to install a driver -- install the Windows 7 DRIVER (x-86 or x-64 depending on what version of Windows 7 you are using).
You should find you can print from your laptop now.
Connect this as a LOCAL printer as described and use the proper Windows 7 driver.
You CAN'T connect x-86 drivers on x-64 Windows 7 systems in any case.
You should be able to find the Laserjet driver on the HP site.
The x-64 Vista one will work as well if it exists.
BTW this is the standard method for getting Windows 7 x-64 machines to share printers attached to win XP and vice versa as wll as for connecting to "network" printer devices.
I know its confusing as the printer is a Network printer and you are poodle faking it to be a "local" printer -- but it's the same sort of confusion as trying to find out what the English mean by a "Public School" -- it's not in any way shape or form what most people would imagine as "Public".