Here's the full crash log:

 

Spoiler

---- Minecraft Crash Report ----
// I just don't know what went wrong

Time: 8/11/17 12:33 PM
Description: Initializing game

org.lwjgl.LWJGLException: Pixel format not accelerated
    at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)
    at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)
    at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)
    at org.lwjgl.opengl.Display.createWindow(Display.java:306)
    at org.lwjgl.opengl.Display.create(Display.java:848)
    at org.lwjgl.opengl.Display.create(Display.java:757)
    at org.lwjgl.opengl.Display.create(Display.java:739)
    at net.minecraft.client.Minecraft.createDisplay(Minecraft.java:689)
    at net.minecraft.client.Minecraft.init(Minecraft.java:499)
    at net.minecraft.client.Minecraft.run(Minecraft.java:416)
    at net.minecraft.client.main.Main.main(Main.java:118)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at net.minecraft.launchwrapper.Launch.launch(Launch.java:135)
    at net.minecraft.launchwrapper.Launch.main(Launch.java:28)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at net.minecraftforge.gradle.GradleStartCommon.launch(GradleStartCommon.java:97)
    at GradleStart.main(GradleStart.java:26)

A detailed walkthrough of the error, its code path and all known details is as follows:
---------------------------------------------------------------------------------------

-- Head --
Thread: Client thread
Stacktrace:
    at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)
    at org.lwjgl.opengl.WindowsPeerInfo.choosePixelFormat(WindowsPeerInfo.java:52)
    at org.lwjgl.opengl.WindowsDisplay.createWindow(WindowsDisplay.java:247)
    at org.lwjgl.opengl.Display.createWindow(Display.java:306)
    at org.lwjgl.opengl.Display.create(Display.java:848)
    at org.lwjgl.opengl.Display.create(Display.java:757)
    at org.lwjgl.opengl.Display.create(Display.java:739)
    at net.minecraft.client.Minecraft.createDisplay(Minecraft.java:689)
    at net.minecraft.client.Minecraft.init(Minecraft.java:499)

-- Initialization --
Details:
Stacktrace:
    at net.minecraft.client.Minecraft.run(Minecraft.java:416)
    at net.minecraft.client.main.Main.main(Main.java:118)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at net.minecraft.launchwrapper.Launch.launch(Launch.java:135)
    at net.minecraft.launchwrapper.Launch.main(Launch.java:28)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at net.minecraftforge.gradle.GradleStartCommon.launch(GradleStartCommon.java:97)
    at GradleStart.main(GradleStart.java:26)

-- System Details --
Details:
    Minecraft Version: 1.12
    Operating System: Windows 10 (amd64) version 10.0
    Java Version: 1.8.0_144, Oracle Corporation
    Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation
    Memory: 866575344 bytes (826 MB) / 1038876672 bytes (990 MB) up to 1038876672 bytes (990 MB)
    JVM Flags: 3 total; -Xincgc -Xmx1024M -Xms1024M
    IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
    FML: 
    Loaded coremods (and transformers): 
    Launched Version: 1.12
    LWJGL: 2.9.4
    OpenGL: ~~ERROR~~ RuntimeException: No OpenGL context found in the current thread.
    GL Caps: 
    Using VBOs: Yes
    Is Modded: Definitely; Client brand changed to 'fml,forge'
    Type: Client (map_client.txt)
    Resource Packs: 
    Current Language: ~~ERROR~~ NullPointerException: null
    Profiler Position: N/A (disabled)
    CPU: <unknown>

 

The standard response to this is to disable the splash screen, but for some reason the config folder with splash.properties doesn't generate for me. The "run" folder specified by runDir contains just logs, crash-reports, and mods, there's no config folder. 

 

I manually created a config folder in the run directory, then copied the splash.properties from .minecraft/config, and disabled the splash screen. That didn't work.

 

I also tried downgrading the java version I use in Eclipse through Windows -> Preferences -> Installed JREs, then selecting jres for both java 7 and 6 (I tried both). Both didn't work either.

 

I'm using Intel HD Graphics, which I know is crap, but I don't have any issues whatsoever running Minecraft modded or not. I also reinstalled the driver.

 

Is there any way to fix this problem or am I straight out of luck?

If I would guess, I would say that there is a problem finding OpenGL drivers which could be caused by out-of date drivers or

something is wrong with the drivers. I would recommend uninstall the driver with something like DDU to make sure everything is removed

uppon uninstallation and then install it again.

Downgrading Java should definitly not solve the problem. Also since Mojang enforces Java 8 with Minecraft 1.12, you shouldn't be

able to start Minecraft with Java 7/6 or lower.