Connection issue to network printer

[DeAwnaMom]

Product Name:  HP Pavilion dv7 running Windows 7 Home Premium 64-bit OS,

HP Pavilion dm4 running Windows 7 Home Premium 64-bit OS,

Dell Precision M65 Windows 7 Professional 32-bit OS

Desktop Computer running WIndows 7 Ultimate, 64-bit OS

HP Officejet 5510 all-in-one printer

Network router:  Netgear N600 Wireless Dual Band Router WNDR3400

Workgroup name one all computers:  WORKGROUP

Issue 1:  Error Message on HP Pavilion dv7 "\\(computer name) is not accessible.  You might not have permission to use this network resource.  Contact the administrator of this server to find out if you have access permissions.  The specified network provider name is invalid."

Issue 2:  dv7 will not print from network printer.  Doesn't even recognize the printer.  But access the internet flawlessly from the network router.

Very frustrated.  After spending over 4 hours on the phone with HP support (with them taking over my laptop to see if they could figure out the issue), then the remained of my day surfing the internet trying to figure out why my laptop will not "see" the network printer at my home I come here to see if any of you tech experts can help with my problem. First let me identify my computers.

Computer 1:  Main desk top computer running Windows 7 Ultimate 64-bit OS, Name:  Desktop1

Computer 2:  (problem child) HP Pavilion dv7 running Windows 7 Home Premium 64-bit OS, Name: dv7bigpc

Computer 3:  HP Pavilion dm4 running Windows 7 Home Premium 64-bit OS, Name:  dm4littlepc

Computer 4:  Dell Precision M65 Windows 7 Professional 32-bit OS

Computers 1, 3, & 4 all see and can access files from Computer 2.  However, Computer 2 can not access files from 1, 3, & 4.  In the HomeGroup window on Computer 1, 3, & 4 only Computers 1, 3, & 4 show up, but down in Network I can see all computers, even Computer 2. 

On Computer 2 on the Homegroup screen I can see computers 1, 3, & 4.  And in the Network list I can also see all the computers listed 1-4.

When I select and click on Network Computer 1, 3, & 4 from computer 2 I get a message "\\(computer name) is not accessible.  You might not have permission to use this network resource.  Contact the administrator of this server to find out if you have access permissions.  The specified network provider name is invalid."  All four are connect to the same workgroup name.

Help!  HP's phone support solution was to buy a wireless printer from them for a discounted rate of $125 to $250 or spend an additional $59 for tech support when I already have the extended tech support purchased for the problem computer.  Although a new air printer would be awesome my current printer works fine and 3 of the 4 computers can print wirelessly(via the network) without any problem.  Even Computer 2 can print from it when it is hardwired to it.  So I really don't think it's a printer issue.  Phone support suggested that the dv7's had some printer issues when they first came out with older printers.  And they suggested that might be why my newly purchased dm4 is printing and connecting via the network without any problems - that hp worked out the "bug" from the dv7's to the current model dm4.  That being said, I'm still open to suggestions and can I get a "patch" or updated driver that would allow my dv7 to connect.  I can't figure out if this is a Windows, HP, Homegroup or other issue.  Even my husband IP guy can't figure out why my laptop isn't able to print when all the others can.

[palspep]

My HP dv7 laptop does not see any printer connected to it by a cable.  I was able to use it with an Epson workstation on Wi-fi .  Am now trying to connect it to a Canon all-in-one wi-fi machine which requires a cable connection temporarily but it still does not work with a cable.  Has anyone figured out what is the problem here and what to do about it?