[AT&T Galaxy Note 3 Q&A, Help & Troubleshooting] Rukbat:
You don't need a program to do that, you need a length of Ethernet cable with connectors on the ends. Unless your laptop is really old it has an Ethernet jack. Just plug the cable into that, and plug the other end of the cable into the modem. Or plug it into one of the connectors on the router if it's just a wifi issue. You have 3 options - wifi, Ethernet connection to the router or Ethernet connection to the modem. Windows will grab an IP address from the router if you're doing it that way (wired or wifi) or from your provider (if you connect to the modem). How connecting the laptop to the modem will eliminate problems with the phone is something I'm confused about, unless you're going to use the laptop as a wifi hotspot for the phone. That's a program I can't help you with. I did an exhaustive search for that kind of setup about 2 years ago, and there was no cheap way to do it. (There's a company that has a box and software, but if you think a Note 3 bought outright is more than pocket change ... $5,000? $6,000? Something in that neighborhood.)

As far as your other problem - the phone not getting wifi from your router? (Whether your internet connection to the router is solid or not has nothing to do with whether the phone is connecting to the router via wifi. I can connect to a wifi router that's not connected to the internet at all. It'll cause "unable to connect" type messages from every app that needs an internet connection, but it'll still be connected to the router.

So, there are a few things you need to figure out. Try Data ON-Off, a free app for the phone. That will allow you to turn your AT&T (3G/4G) data off so, good signal from wifi or not, your phone won't use AT&T.

Use Wifi Analytics (another free app) to ssee what's going on there. If there a few wifi signals on the same channel as yours, you may be getting so much interference that the phone can't see your router's signal and drops that connection. (Changing channels on the router depends on which router you have, but it's in the wifi section and it's simple - usually just a dropdown for channel number. Wifi Analytics lists the channels as poor, good and best based on what signals are on what channel. Use one of the ones marked best, or at least good.)

It also depends on what's between you and the router. In my last house, if I was on the deck and someone turned on the microwave, I lost the internet. The physical path from my seat on the deck to the router passed right through the microwave. Little metal box, not much signal loss. But when it was running it wasn't a little metal box, it was a huge 2.4GHz transmitter, transmitting (as far as wifi is concerned) garbage and noise. I didn't mind 30 or 60 seconds of loss of signal, I'd just refresh the page when the microwave was done. But my wife, who plays WoW, would want to get safe before I ran the microwave. 5 seconds of no signal and you can get killed there. (She may be the only player ever on WoW who died when she was dead. Something like she got killed PvP at the edge of a lake, fell in and drowned. Drowned while she was already dead.) If the path from your phone to your router is through a lot of walls, that's a problem too. Each piece of sheet rock only absorbs a little signal, but a few walls together can kill it. Same thing if the path is through a large piece of metal, like a refrigerator. Or if your router antenna is vertical and you're on the floor above it. (Antennas shoot at right angles to their axes.)

This is the kind of thing that drives microwave engineers mad. If you're going for minimum power needed for the path loss, and you didn't notice that tree in the path in December, come May when the tree has leaves you lose the signal, and thousands of customers scream. Oops. (It's also why some satellite TV systems don't work very well when it's pouring rain. They didn't calculate the additional path loss. "It never rains, does it?")

But understand, the strength of your internet signal (Exede to your modem) has nothing to do with the strength of the signal from your router to your phone over wifi. Think of a radio station. The announcer is so close to the mic that his lips are touching it, and he's shouting. But you're MANY miles away and can barely hear the station through the static. Or, the other way around, you live right near the transmitter, but the announcer is in the room next to the mic and he's mumbling. In each case one part of the "signal path" (which included announcer to mic and transmitter to receiver) is good but the other one isn't. Your Exede to modem path is good, but something between there and the phone is bad.

So if you still want to use wifi from your router, you may now have enough information to figure out why it's not solid connection, and maybe enough to change what needs to be changed to make it work. (Moving 2 feet left [or whatever] may be enough to increase the signal enough to give you a solid connection on wifi if, looking from where the phone isn't working well to the router [with X-Ray eyes], you see a refrigerator or something..)