Lost ip/connection on Dell 1720dn

The printer's IP address most likely needs to be changed.
Check the Belkin's IP address range (it maybe 192.168.2.***) and configure the printer's IP address accordingly.

When the Ready/Data light is solid, press the Continue button to print a menu settings page and a network setup page.
Select TCP/IP heading on the network setup page.
There you can change your IP address.

check for the drum and toner maybe it need a replacement

I Open my browser....I signed in to my router as administrator ....
Mine is 192.168.1.1 ....
I went to status in my router ....
Then to local network ....
Then to DHCP Clients Table ....
This is how I found what printer address the was.... Then I typed the printer ip address into my browser
Mine happened to be 192.168.1.105 ....
Yours will probably be different....That got me to the 1720dn printer menu ....I clicked on Configuration ....
I clicked on Print Server Settings
I clicked on TCP/IP
I clicked on Set static IP address.
I changed IP address from 192.168.1.105 To 192.168.1.125
and Submit....Now you can get to the printer menu at 192.168.1.125

Go to run....
Printers & Faxes
Right click on Dell laser printer 1720dn
Properties. Ports ....
Add port ....
Double click on Dell Enhanced TCP/IP ....
I named the port My dell laser 1720 dn....Where it said enter a single IP address or host name I entered the new address 192.168.1.125
the clicked OK ....

Right click on Dell laser printer 1720dn
Properties....Ports
Choose your new port ....

I did a forced reset to default... Open the front panel, hold down the green and orange buttons, turn on the printer. Wait as the lights cycle until the error light remains on, then close the front panel. A new config page will print, and then you will be able to connect to the printer using the new DHCP address that has been assigned.

Open the back cover and look for paper wrapped around a roller back there. That is the most common cause of the issues with this machine. The other thing you can try is to push down on the little flaps where the paper comes out of the printer. These get stuck and need cleaning/replacement all the time in the later life of these models (1720's).

Around the office, your laptop is probably connected to a wireless network which you don't have at home. To connect, you would need to connect to the office network from your home through a VPN (Virtual Private Network) over the Internet or through a dial-up (ugh!) connection to the office systems. Your office IT staff should be able to help you get that set up since either way it would require some configuration on their end to allow you to connect remotely to the office systems.

this printer is (as per HP specs) only connected via USB or Wlan Print server.
Check connection using USB cable and be sure Printer driver are correctly working.
Check on Router your Print server IP address (Lock it out of DHCP)
Put both PRT and PC on same home network (normally HOME or MSWORK)
Put Printer server IP address into your printer properties/port tab/ IP.
OR check if you see your printer server in your Windows network/home network

Open a browser and type in htp://192.168.0.1 to access your router's web management interface. Enter the username and password (default is username admin and no password)
Go to the Advanced Tab and Virtual Server
Name=VNC
Private IP=IP Address of your Home notebook
Protocol Type=TCP
Private Port=5800
Public Port=5800
Set Schedule as you like
Enable the rule and click Apply.

To access you Home notebook from anywhere other than your house, go to http://10.0.57.46:5800

Next - remote management of the router.
The IP address that you enter on the remote management page is the IP address that is allowed to connect to the remote management. If the 194.145.183.83 is the IP address of your office, this should work. Be sure you apply a password or anyone going to http://10.0.57.46 will have access to you router, I also recommend changing the port from 80 to 8080 so that http://10.0.57.46:8080 has to be typed to access the remote management interface.

As far as your primary connection is DHCP and when its detects wireless conecction it will start getting to connect to the device becoz in you configuration you choose connect to any wireless access point option. At office your laptop try to connect but the secondary Ip address and primary configuration get conflict and primary configuration ask you to repair or shows limited connectivity option. Better is enable dhcp on you both sides so that you will not face any problems