Before you get into anything complex, it’s a good idea to get started with the basics. If you find that an application won’t open, make sure that it’s not a problem with your desktop shortcut. Instead of launching the Epic Games launcher from its usual spot, go to your Start Menu and launch the application from there.

Well, the launcher should open, and I'm not positive why it isn't. It could have something to do with any anti-virus you have trying to block it from connecting to the internet. What I would do is try to open the launcher, then open the task manager (using Ctrl + Shift + Esc) and under Apps, you should see EpicGamesLauncher. If you don't, something's wrong. If this is the case, I'd try temporarily turning off your anti-virus. Make sure you turn it back on later If this works, close the launcher, turn your anti-virus back on, and look for something call exceptions or whitelist under your firewall. Add the launcher to that whitelist.

Epic Games Launcher Not Opening Windows 10

Epic Games Launcher Not Loading

On a different note, the Intel HD Graphics is an integrated graphics card, and while that wouldn't prevent the launcher from opening, it will make using UE4 difficult. You'll have to set the Engine Scalability Settings to low if you want it to run well because integrated graphics cards are simply not up to the task of running game engines like UE4. My suggestion is to get a GTX 1050 Ti (it costs around $150). If you have any questions about the graphics card stuff, feel free to ask.