Ethernet printer won't print with WIFI on.

you can look into this but you may want to ask HP about compatibility.

http://www8.hp.com/us/en/products/print-servers/product-detail.html?oid=5371954

http://store.hp.com/us/en/hp-jetdirect-

I understand you need to print tabloid (and what a decent tabloid printer can cost you these days) but that printer is old as far as HP is concerned and my have very limited options outside of a print server if some wireless Jet Direct option does not interface with it. My experience with Jet Direct ended around the same time we started getting ethernet printers on site.
If you can get the printer near the router or vice versa it's definatly removing some potential points of failure and would the the recommend (by me) course of action.

A Cat6 ethernet cable has a theoretical limit of 300 ft or 90 meters last time I looked.

AppleTalk is no longer used and having the protocol active on the printer may be causing problems if you are no longer in an AppleTalk environment. You should be printing over IP over the router via ethernet or if it supports USB it's also a possibility.

Alternatively, is there a device I can attach to my printer so I can print from any computer in the house instead of having it hardwired into my Macbook Pro? I've tried it with an Airport Express, but couldn't get it to work.

Are you using your Mac as a print server? If the HP has ethernet you should connect it to the router via ethernet, or if your router supports a USB device you can connect it though that. You will need to configure the printer via IP address of the router (possible 192.168.1.1)

if that is not possible you may need an HP Jet Direct card to turn the device into a network printer.

The issue is the IP address you are using for the printer and the Ethernet port. Since the WiFi is using the 192.168.0 subnet, then you cannot use the same subnet for the printer. This is because the Mac will attempt to use the WiFi connection to the router (192.168.0.1) whenever you attempt to connect to the printer on 192.168.0.10. Does the new router have an Ethernet port? Because your best solution is to connect the HP via Ethernet to the router and then let it allocate an IP address to the printer using DHCP. Or you can manually reserve an IP address for the HP if needed via the network settings of the router.

With regards to the AirPort Express, then the most likely reason that did not work is that it was not an extension of the current WiFi. You would need to set it to bridged mode so that it uses the network settings provided by the main router. Then you could connect the printer to the Ethernet port of the Express (assuming the model you have does have an Ethernet port). And then like above you should set the printer to DHCP. This just ensures its address is in a range used by all the network devices.

As for the current setup, the solution would be to change the IPv4 address being used by the Ethernet port on the Mac and the printer. For example, if you set the Ethernet port at 172.16.1.1 and the HP at 172.16.1.10 (leaving the subnet mask at 255.255.255.0) then you should be able to connect to the printer while using WiFi.