@slowRouter 

Leave the computer awake, disconnect it and then reconnect connect it several minutes later. Does the internet connection work quickly?

If that works normal it has to do with the computer in it starting up, then acquiring and internet connection.

What you describe is what other people report with their computers as well when searching online: Link

@Tony Actually if I disconnect the computer and reconnect I get the same delay before the internet connects.  It's about 10-20 seconds, just enough to be annoying.

I also messed around with the network card power settings and didn't get anywhere with that.

What power settings? Is the NIC set to allow it to turn-off to save power in the Properties? Is the computer coming out of sleep when this happens?

Also, the power bus could be powered down during sleep, there is a setting in the power plan to change this.

@IrvSp I disabled the power saving feature.  I also tried an update of the network card driver.  Yes it's coming out of sleep when this happens.

I took a look at windows 10 power options advanced.  Changed Wireless Adapter Settings and PCI Express both to maximum performance but that still didn't work.  Is that what you were getting at?

By the way, this problem started immediately after switching routers.

@slowRouter ,

Yes, I was thinking a power plan setting.

Network adapter on the motherboard or external? USB? Power settings for that need to be changed too.

Next place to look is the Security suite I guess? Disable that for a few minutes, put the pc to sleep and then wake up and see what happens.

New router only? Was the IP Address changed from the old router? Have 2 possible connections for the device? I'd delete them all and redo the connection and see if that helps?