How do I detect keyPress while not focused?

Well, if you had problems with System hooks, here is ready-made solution (based on http://www.dreamincode.net/forums/topic/180436-global-hotkeys/):

Define static class in your project:

public static class Constants
{
    //windows message id for hotkey
    public const int WM_HOTKEY_MSG_ID = 0x0312;
}

Define class in your project:

public class KeyHandler
{
    [DllImport("user32.dll")]
    private static extern bool RegisterHotKey(IntPtr hWnd, int id, int fsModifiers, int vk);

    [DllImport("user32.dll")]
    private static extern bool UnregisterHotKey(IntPtr hWnd, int id);

    private int key;
    private IntPtr hWnd;
    private int id;

    public KeyHandler(Keys key, Form form)
    {
        this.key = (int)key;
        this.hWnd = form.Handle;
        id = this.GetHashCode();
    }

    public override int GetHashCode()
    {
        return key ^ hWnd.ToInt32();
    }

    public bool Register()
    {
        return RegisterHotKey(hWnd, id, 0, key);
    }

    public bool Unregiser()
    {
        return UnregisterHotKey(hWnd, id);
    }
}

add usings:

using System.Windows.Forms;
using System.Runtime.InteropServices;

now, in your Form, add field:

private KeyHandler ghk;

and in Form constructor:

ghk = new KeyHandler(Keys.PrintScreen, this);
ghk.Register();

Add those 2 methods to your form:

private void HandleHotkey()
{
        // Do stuff...
}

protected override void WndProc(ref Message m)
{
    if (m.Msg == Constants.WM_HOTKEY_MSG_ID)
        HandleHotkey();
    base.WndProc(ref m);
}

HandleHotkey is your button press handler. You can change the button by passing different parameter here: ghk = new KeyHandler(Keys.PrintScreen, this);

Now your program reacts for buton input even if not focused.

The API GetAsyncKeyState() may be a perfectly acceptable alternative to setting up Windows Hook.

This depends on how you desire to receive the input. If you prefer event-driven notifications, then a hook is the way to go; however, if you prefer polling the keyboard for state changes, you can use the API above.

Here is a simple demonstration of how to use GetAsyncKeyState:
^{Derived from Pinvoke.NET}

[DllImport("User32.dll")]
private static extern short GetAsyncKeyState(int vKey);

private static readonly int VK_SNAPSHOT = 0x2C; //This is the print-screen key.

//Assume the timer is setup with Interval = 16 (corresponds to ~60FPS).
private System.Windows.Forms.Timer timer1 = new System.Windows.Forms.Timer();

private void timer1_Tick(object sender, EventArgs e)
{
    short keyState = GetAsyncKeyState(VK_SNAPSHOT);

    //Check if the MSB is set. If so, then the key is pressed.
    bool prntScrnIsPressed = ((keyState >> 15) & 0x0001) == 0x0001;

    //Check if the LSB is set. If so, then the key was pressed since
    //the last call to GetAsyncKeyState
    bool unprocessedPress = ((keyState >> 0)  & 0x0001) == 0x0001;

    if (prntScrnIsPressed)
    {
        //TODO Execute client code...
    }

    if (unprocessedPress)
    {
        //TODO Execute client code...
    }
}

Yes you can, it's called "System hooks", take a look at Global System Hooks in .NET.