Photosmart C4780 says wireless is on but computers say printer is not connected

Question

My Photosmart C4780 has always been temperamental with its wireless network connection; I have had the printer replaced once already and with both machines spent several days worth of hours on the phone to HP Helpdesks trying to uninstall and reinstall the drivers and additional software for various issues - either printer or scanner not working.
Now the problem is that although the thing itself says that the wireless connection is on and working fine; none of the computers on my home network (Two PCs running Windows 7 32-bit; and two Macs running OS X Lion) are able to connect to the printer; no matter what I try it keeps saying the printer is offline.
I would happily throw the thing in the rubbish bin to stop wasting any more time on it; but I have just bought 5 new (original HP  XL) cartridges for it and would hate to waste those.
In fact the problems started when I replaced the cartridges; the alignment page at first refused to scan and when it did, it came up with an error message which unfortunately I can no longer remember exactly; something about the thing not being properly aligned and this may affect print quality.  I am assuming that this is what caused the problems; although why this would cause the computers on the network to say that the printer is offline I have no idea.  It has printed scanned images since then which came out fine; so the print quality can't have been that badly affected.
Anyway, the thing is too old now to be able to call the HP helpdesk again (all of about two years old!) so I really don't know what else to do - apart from binning it and trying to get a refund on the three unused cartridges.  Oh, and buying a different make printer, obviously!  
I have previously had a Photosmart 7350 which worked beautifully for many years, until I upgraded the computer to Vista and HP could not be bothered to provide updated drivers for it. The print quality of this one was what made me decide to go for HP again - a decision I seriously regret now!
Does anyone have any ideas of how to get the thing working again; at least until I have time to properly research an alternative?
Thank you 

Answer 1

SafeTouch wrote:
Thank you PrintDoc.  I'm afraid I don't completely understand your instructions.  I found the page you said to set a manual IP address, but then I got stuck:
When you say: "You need to set an IP address outside the range that the router automatically sets (called the DHCP range). If you do not know the range, change the last set of numbers (those after the last '.') to 250" what exactly do you mean?   All boxes on this page are completely blank; so what address should I put here?  Put the same address as the printer currently has, only substitute another number (like 250) for the number after the last '.' in the printer's current IP address.
And when you say: "Enter your router's IP (on the Network Config Page) for the gateway." are you talking about the IP address that is printed in the confuguration summary underneath 'network name (SSID)' and 'hardware address (MAC)' as 'IP address'?  Or would this be the address to put in above?  The gateway address will be the same as the printer's, but will end in .1
Thank you for your help so far; please clarify this.
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I am employed by HP