Problem printing over local network

[#1]

I have a wired, ethernet, home network that I'm trying to attached a printer to but it won't print. The system is basically a Thompson TG585 v7  ADSL router from PlusNet with default setup, its lan ports connect to 16 way switches which then have cables running throughout the house to sockets.  A HP Lazerjet 2300 with a JetDirect card (with IP address of 192.168.1.73) is plugged into one of these sockets.
Trying to print from two different netbook computers, one running Windows 7 Light other Windows NT. Setup trying to use TCP/IP port with correct driver.  Printer is always shown as offline, but I can bring up the printer using the IP address in Internet Explorer to see its configuration just fine.  Using windows, find / add printer it is never found.
Wondering if the TG585 is blocking access.  Have tried it on a different but similar network with a different ADSL modem/router (using one of same Netbooks) and in 10 min can have a similar HP Lazerjet printing just fine. 
Any help would be much appreciated.  I'm not all that network knowledgeable so need details in any instructions.  Oh, can see the lan network, ie copy files between netbooks, as well as internet so some of it is working OK.

[#2]

The router plays no part in the traffic between your PCs and your printer, other than issuing the IP addresses to your machines.
What addresses do your PCs have?  I'm assuming the 192.168.1.73 address for the printer is static and has been configure manually?  Not a good idea configuring it in the same range as the router can hand out via DHCP.
Try moving the printer to something like 192.168.1.253, setting a PC up as 192.168.1.252 testing again.  You can prove the router is not involved by removing the connection from the LAN port to your switch.

[#3]

Oops, a typo - the router modem is the TG582n  not TG585.  I hadn't expected this to block the printer, but it has a built in firewall which seems to have some odd things it does and its router table doesn't seem to cover the full 255 range.  I'm not at the house at the moment so can't check.  The Windows 7 Netbook I think is on 198.168.1.66 so in the same range as the printer.

[#4]

The firewall only applies to WAN<>LAN traffic - The communication path between the printer and the PC is just via your 16 port switch.
HTH

[#5]

I suggest assigning the printer a fixed IP *below* the router's DHCP range which starts at 192.168.1.64 . For example 192.168.1.32 . I'd avoid 192.168.1.253 since that is sometimes associated with router FTP access.

[#6]

Turn the printer off and try and ping 192.168.1.73 if no reply then turn on and ping again, just to check there is not another device on the same address.
As above not a good idea to have within the router's DHCP range, so worth reconsidering that.
I had a similar "off Line" problem with a HP M551 laser and ended up downloading bare drivers from HP and installing them rather than the automated install off the supplied CD

[#7]

OK, when I am back at the house will set the printer to a lower IP address, after checking its current address for conflict.  Thanks for info on router firewall, I should probably also check the firewall on the computer but think that is OK as it connects to the lan and printer at work.

[#8]

I have a very similar setup. I got over this problem by just ticking the box "Always use same IP address" on the 582n when connecting the printer and setting the printer to get its IP address automatically.
My printer is currently assigned 192.168.1.68.

[#9]

  Great it worked. Set the printer to manual instead of auto and IP address of192.168.1.35 on the printer.  I don't understand why, but moving off the routers DHCP range did the trick.  Strange not a problem on office router.  Thanks everyone.