Had to look in the logs for this one.
An error occurred trying to configure the minecraft home at C:\Users\augitesoul\Desktop\Apocalypse for Forge Mod Loader
java.lang.NoClassDefFoundError: net/minecraftforge/fml/relauncher/IFMLLoadingPlugin
at java.lang.ClassLoader.defineClass1(Native Method) ~[?:1.8.0_25]
at java.lang.ClassLoader.defineClass(ClassLoader.java:760) ~[?:1.8.0_25]
at java.security.SecureClassLoader.defineClass(SecureClassLoader.java:142) ~[?:1.8.0_25]
at java.net.URLClassLoader.defineClass(URLClassLoader.java:455) ~[?:1.8.0_25]
at java.net.URLClassLoader.access$100(URLClassLoader.java:73) ~[?:1.8.0_25]
at java.net.URLClassLoader$1.run(URLClassLoader.java:367) ~[?:1.8.0_25]
at java.net.URLClassLoader$1.run(URLClassLoader.java:361) ~[?:1.8.0_25]
at java.security.AccessController.doPrivileged(Native Method) ~[?:1.8.0_25]
at java.net.URLClassLoader.findClass(URLClassLoader.java:360) ~[?:1.8.0_25]
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:117) ~[launchwrapper-1.12.jar:?]
at java.lang.ClassLoader.loadClass(ClassLoader.java:424) ~[?:1.8.0_25]
at java.lang.ClassLoader.loadClass(ClassLoader.java:357) ~[?:1.8.0_25]
at java.lang.Class.forName0(Native Method) ~[?:1.8.0_25]
at java.lang.Class.forName(Class.java:344) ~[?:1.8.0_25]
at cpw.mods.fml.relauncher.CoreModManager.loadCoreMod(CoreModManager.java:460) ~[forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.relauncher.CoreModManager.discoverCoreMods(CoreModManager.java:389) ~[forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.relauncher.CoreModManager.handleLaunch(CoreModManager.java:221) ~[forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.relauncher.FMLLaunchHandler.setupHome(FMLLaunchHandler.java:90) [forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.relauncher.FMLLaunchHandler.setupClient(FMLLaunchHandler.java:67) [forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.relauncher.FMLLaunchHandler.configureForClientLaunch(FMLLaunchHandler.java:34) [forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at cpw.mods.fml.common.launcher.FMLTweaker.injectIntoClassLoader(FMLTweaker.java:126) [forge-1.7.10-10.13.4.1614-1.7.10.jar:?]
at net.minecraft.launchwrapper.Launch.launch(Launch.java:115) [launchwrapper-1.12.jar:?]
at net.minecraft.launchwrapper.Launch.main(Launch.java:28) [launchwrapper-1.12.jar:?]
Caused by: java.lang.ClassNotFoundException: net.minecraftforge.fml.relauncher.IFMLLoadingPlugin
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:191) ~[launchwrapper-1.12.jar:?]
at java.lang.ClassLoader.loadClass(ClassLoader.java:424) ~[?:1.8.0_25]
at java.lang.ClassLoader.loadClass(ClassLoader.java:357) ~[?:1.8.0_25]
... 23 more
Caused by: java.lang.NullPointerException
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:182) ~[launchwrapper-1.12.jar:?]
at java.lang.ClassLoader.loadClass(ClassLoader.java:424) ~[?:1.8.0_25]
at java.lang.ClassLoader.loadClass(ClassLoader.java:357) ~[?:1.8.0_25]
... 23 more

reinstall forge

still not working

First of all, I see nothing related to Mekanism in your logs. But my guess is, outdated Forge. Can't help much more without some specific version numbers, a whole log, a modlist.

I have the latest Forge reinstalled, with removal of all config files, and I'm also getting a crash

What version of Forge I need? It's doing that with 1614 too.
Log:http://pastebin.com/dxxRiA8F
Modlist is linked.
modlist.txt

A completely fresh install of Minecraft - to remove all possible files - and as soon as I add Mekanism Core it crashes.

edit: and indeed, forge, with only Mekanism crashes.

[19:29:54] [main/WARN]: The coremod mekanism.common.launch.LoadingHook does not have a MCVersion annotation, it may cause issues with this version of Minecraft

Only thing I can see in the log

Using an nVidia Card? [https://github.com//issues/4205]

@AugiteSoul You have a double mekanism in your mod folder. Mekanism 1.7.10 and Mekanism 1.10.2. Please remove the 1.10.2 version

Nice, you seen something that I didn't see. Thanks!