In order to use your theme you need to add and set an alternative for the default plymouth theme, and update the initramfsinitrd image.
sudo update-alternatives --install /lib/plymouth/themes/default.plymouth default.plymouth /lib/plymouth/themes/dell/dell.plymouth 75
sudo update-alternatives --set default.plymouth /lib/plymouth/themes/dell/dell.plymouth
sudo update-initramfs -u
You can also test your theme without rebooting by using plymouthd and plymouth.
sudo apt-get install plymouth-x11
sudo plymouthd
sudo plymouth show-splash
Edit: Here's the slightly modified dell.script that I used for testing:
Window.SetBackgroundTopColor(0.91, 0.92, 0.91);
Window.SetBackgroundBottomColor(0.80, 0.80, 0.80);
screen.width = Window.GetWidth();
screen.height = Window.GetHeight();
dell.image = Image("wallpaper.png");
dell.width = dell.image.GetWidth();
dell.height = dell.image.GetHeight();
if(dell.width < dell.height) {
dell.ratio = screen.height / dell.height;
dell.x = Math.Abs(screen.width - (dell.width * dell.ratio)) / 2;
dell.y = 0;
} else {
dell.ratio = screen.width / dell.width;
dell.x = 0;
dell.y = Math.Abs(screen.height - (dell.height * dell.ratio)) / 2;
}
dell.scaled = dell.image.Scale(dell.width * dell.ratio, dell.height * dell.ratio);
dell.sprite = Sprite(dell.scaled);
dell.sprite.SetX(dell.x);
dell.sprite.SetY(dell.y);