HP 6600. I always get the issue scanner unreachable

Question

When I go to scan a document or photo, I get the error, scanner unreachable. When I try manage scan to computer, I get, scan to computer is unavailable.  When I go to my printer, sometimes my computer is not listed, sometimes it is. It is currently listed, so I tried to scan from there, I get error messages.
I have been having this problem for over a year. I bought this printer  June of 2013 for its feeder scan. It seemed to work fine.  Then we moved in Nov 2013, and it has not worked since then, So it makes me wonder if it is my internet, My internet provider tells me they know it is crappy and they are working on it, but I have no other choice. It is very spiky.  I have tried the HP doctor, and since I had to update it  to 4.6 yesterday,it doesn't work, it finds my printer and then it says it has stopped working. But who knows, tomorrow it may work. 
Tried using the printer home page feature, 10 minutes ago, itwas something like web page not found, but now it is working, I tried  scan to computer there, and it says You cannot use this function because it has been disabled. For more information, contact your network administrator or the person who set up the printer. 
Good thing, I still I have my Epson scanner, which I usually use for printing and scanning, because I have no issues with it. But I want to scan multiple pages of documents. 
Update: tried to scan from printer again, computer not listed again. uggggghhhh. Can someone help me with this. 

Answer 1

June,
Printers are not all equal.  Routers are the same: some are better than others.  That is why it is a balancing game, even given that one has a decent network to begin with.  I don't know whether your network is OK or not -- I don't have the tools, the time, nor the inclination to delve into it that deeply.  I am not being rude -- you are in a tough spot if you don't have decent ISP service because the onus falls on you to know more than the average home user needs to know about his / her network.  The information is out there; it can be a real mess to wade through it and figure out what is going on.
In General, printers work better than this.  In general, networks are not flakey.  Of course, based on the number of complaints you see on forums, you would think nothing works - ever.  But there are millions of working printers and networks all over the world and people don't complain about stuff that works.
Plus, and this is the most important bit:  I am not a Printer Expert.  I have advice that I hope will help you track down an improvement in your situation.  I have been known to be wrong.  What was left of my ego was left shredded on the cold tiles of an IT Server room decades ago the first time I crashed a network.    
So.. you may have a flakey network because of stuff you cannot control.
Yes, I hated the cable idea anyway.  Smiling.  BTW,  we purchased three routers before we found one strong enough to do the job and we moved it twice before we found a spot that it works best for all the devices.  Of course, although the house is small, the property is not and we have a number of devices that we drag about -- you may not need the coverage we needed.  Still, routers do matter.    Read, read, then decide if you have what you want.
The "increasing the power" comes from the Dragon Document:
Settings to Improve Wireless Connectivity
See the section titled:
Lost Wireless signal issues
=================================================================
Just thoughts:
The rest of the setup and Troubleshooting are pretty cut and dried -- and some of it may help.  You will probably benefit from having someone work with you a bit on this, even someone who doesn't know a great deal more than you do -- there is knowledge in having more eyes on a problem.  Get a friend, sit down, read the suggestions, think about what you have tried, what sounds reasonable, what sounds like you can actually DO, and try those things first.
I hope this helps, at least a bit.
Perhaps an actual Printer Expert will step in and have some advice.  Smiling.
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I am pleased to provide assistance on behalf of HP. I do not work for HP. 
Kind Regards,
Dragon-Fur