After 6h spent trying to fix this by myself, AS is driving me crazy. Everything was fine yesterday and today it can't resolve any of the support libs nor the R symbols.

I tried everthing, including all the suggested fixes I found on StackOverflow. No need to tell me to have a look a this post, I already have and none of the solutions work.
Here's what I tried so far :
- rebuilding / cleaning the project (many times...),
 - synchronising the project with Gradle Files,
 - check that the support lib is up-to-date in the SDK Manager,
 - invalide Caches / restart AS,
 - delete the .idea folder and the .iml files of my project, and re-importing it in AS,
 - update AS from 0.8.11 to 0.9,
 - eventually I ended up uninstalling AS and reinstalling it from scratch
 
And none of this fixed my issue...
Something really weird is that I also tried to create a whole new project from scratch and to copy/paste all my classes & resources from my corrupted project to this new one. And it worked for a while (~10 min), until it eventually became corrupted the same way, without any apparent reason.
Moreover, no idea if it's relevant, but when I type "ViewPager" in AndroidStudio and hit CTRL-SPACE, it doesn't suggest me the "android.support.v4.view.ViewPager" class. But if I hit CTRL-SPACE 3 times in a row, it DOES suggest it. So I guess that means that it's able to find the support lib somewhere but not to use it?
Here's my build.gradle :
apply plugin: 'com.android.library'
android {
    compileSdkVersion 21
    buildToolsVersion "21.1.0"
    defaultConfig {
        applicationId "com.mathieumaree.library"
        minSdkVersion 15
        targetSdkVersion 21
        versionCode 1
        versionName "1.0"
    }
    buildTypes {
        release {
            runProguard false
            proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
        }
    }
}
dependencies {
    compile fileTree(dir: 'libs', include: ['*.jar'])
    compile 'com.android.support:appcompat-v7:21.0.0'
    compile 'com.android.support:support-v13:21.0.0'
}
Please, help me, otherwise I'm gonna break my computer soon.
Thanks in advance,
Mathieu
EDIT 1 :
I forgot to mention that this occurs only in one of my projects. The others seem to be fine (at least for now).
EDIT 2 :
I also forgot to mention that my project is composed of an application project plus a library module inside it. So here is the app's build.gradle :
apply plugin: 'com.android.application'
android {
    compileSdkVersion 21
    buildToolsVersion "21.1.0"
    defaultConfig {
        applicationId "com.mathieumaree.materialheaderviewpager"
        minSdkVersion 15
        targetSdkVersion 21
        versionCode 1
        versionName "1.0"
    }
    buildTypes {
        release {
            runProguard false
            proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
        }
    }
}
dependencies {
    compile fileTree(dir: 'libs', include: ['*.jar'])
    compile project(':library')
    compile 'com.android.support:support-v13:21.0.0'
    compile 'com.android.support:appcompat-v7:21.0.0'
}
The app Manifest :
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.mathieumaree.materialheaderviewpager" >
    <application
        android:allowBackup="true"
        android:icon="@drawable/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >
        <activity
            android:name="com.mathieumaree.materialheaderviewpager.MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />
                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>
</manifest>
The library manifest :
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="com.mathieumaree.library">
    <application android:allowBackup="true"
        android:label="@string/app_name"
        android:icon="@drawable/ic_launcher"
        android:theme="@style/AppTheme">
    </application>
</manifest>
The main settings.gradle :
include ':app', ':library'
And the main build.gradle :
// Top-level build file where you can add configuration options common to all sub-projects/modules.
buildscript {
    repositories {
        jcenter()
    }
    dependencies {
        classpath 'com.android.tools.build:gradle:0.14.0'
        // NOTE: Do not place your application dependencies here; they belong
        // in the individual module build.gradle files
    }
}
allprojects {
    repositories {
        jcenter()
    }
}
EDIT 3 :
After trying once more to delete all .idea folers & *.iml files and reloading my project, I noticed that AndroidStudio displayed an error at openning :
Accessing invalid virtual file: file://C:/Users/Mathieu/AppData/Local/Android/android-studio1/sdk/sources/android-21; original:582; found:-: Accessing invalid virtual file: file://C:/Users/Mathieu/AppData/Local/Android/android-studio1/sdk/sources/android-21; original:582; found:-
I'm pretty sure it means it's looking for the SDK to yet another location (AppData/Local...android-21). What I don't understand is :
- there's no SDK folder at this location
 - the SDK path indicated in the Project Structure is not this one
 
Any idea what all this means?