Basically when you restart your pc windows will load all the drivers again so that's why the network driver is working. When you shut down the pc and then switch it on again the next time it will load a the previous session and will not load the drivers this is done because it will start up windows 10 faster. It is a windows 10 feature call the "fast start up feature".
Are you using the Wired Ethernet 82579 for your dell computer?
Can try these 2 solutions see if it can fix the problem.
SOLUTION 1
From the Win10 start menu choose > SETTINGS > Power & Sleep > Additional Power Settings> "Choose what the power buttons do" > "Change settings that are currently unavailable" > and then UNTICK the "Turn on Fast Start-up (recommended)" box
Basically what's been happening is on Fast start-up it tries to use the previous sessions 'ipconfig', Without the fast start-up, it resets the ipconfig and then loads the network driver from scratch - so it finds your adapter.
(Also... under SETTINGS>DEVICES>Device Manager>Network Adapters> intel..Gigabit Network Connection >(RightClick)Properties>Power Management> UNCLICK "Energy Efficient Ethernet", which will shut down your connection if you don't use it for a while!. )
SOLUTION 2
1. Create a file named NetRenew.bat and place the following commands into it:
@echo off
ipconfig /release
ipconfig /renew
2. Place a shortcut to this file into your Startup folder (i.e. C:\Users\<YourUserName>\AppData\Roaming\Microsoft\Windows\Start Menu\Programs\Startup).
3. Test whether, with this change in place, the problem is alleviated. If it is, then you have a workaround.