Hmmm... I have to admit I usually avoid the problem at this point. So I recommend to people to buy a network printer. They are cheap now.. to the point where purchasing a new toner cartridge for the old printer and buying a new printer are not too different. As btw.. laser jet P1005 is host based. That means there is no page interpreter in the printer.. it is entirely handled by the software driver in the computer.. these are the most difficult printers to use over network.. as the printer was designed from ground up as personal (P means Personal) printer plugged to one computer.
Let me try and work through the problem.
My guess would be that your change of house involved a new modem router which is simply less bonjour aware.
The printer needs to work via bonjour. Since all the other elements stay the same.. that would be where I am guessing the problem lies. Although it is surprising the printer seems to show as available and then shows as disconnected when you actually attempt to print.
I need some details of the network.
1. What OS is the computer running?
2. What is make and model of your main modem router?
3. What model is the Time Capsule?
4. Is the TC plugged into the main router by ethernet and running in bridge mode?
5. Is the computer using the TC wireless or main router wireless for its connection?
6. If the later would it be possible to arrange the TC to provide wireless network you connect to from the computer?
7. Would it be possible to get ethernet to the computer.. via the TC?
Screenshots from airport utility are very helpful and welcome.
My aim would be to change the TC from bridge to router .. but in a special way.. DHCP only with no NAT. And have the computer connect directly to the TC by wireless or ethernet instead of via the main router which I suspect is mishandling the bonjour.