Hello Laura C. I haven't noticed any problems with my wireless connections to my Canon printers, at home or at work, and I have the Update 4 installed. I also cannot think how this update would have impacted your ability to connect to the printer, except maybe due to a reliance of the HP software using Java to operate. But this should not have stopped your existing connection from working, only a new connection...
Apologies in advance if you have already been through the following, but if you were successful in entering an IP address manually, I would then check that you can get a response from the printer. The best tool to use is Ping. Open Applications > Utilities > Network Utility. Here you will see the Ping tab, as well as several other IP tools.
Before you select Ping, select Info (it probably has defaulted to this). This pane shows you the current IP address settings for your Mac. Since you are using wireless, change the drop menu from en0 (which is Ethernet) to en1 (wireless). This will show your current IP address set in the Mac. Make a note of this.
Now select the Ping tab and enter the IP address of the HP. Change the number of pings to 4 and press the Ping button. If the addresses are correct and the network infrastructure working you should get a response. If you get something like " 4 packets transmitted, 0 packets received, 100% packet loss", then that would explain the unreachable message.
The biggest cause of this symptom is subnetting. To explain further, an IP address consists of two parts, the subnet and network address. The subnet is determined by the subnet mask. If you have a subnet mask of 255.255.255.0, the your subnet is the first three sets of numbers in your IP address and the network address is the last number. For example, an IP address of 10.0.1.10 and subnet mask of 255.255.255.0 has a subnet of 10.0.1 and a network address of 10. For devices to communicate on a local network, they typically need to have the same subnet and a different network address. Can you confirm the subnets for the Mac and printer are the same and the network addresses are different.
If you get responses to the Pings, which indicates the IP addressing is okay, the other services like firewalls can stop some printer utilities from working correctly. Have you checked your System Preferences > Security > Firewall setting is set to allow all incoming connections?
HTH
Pahu