Windowed Mode
LEGO Island does not officially have a Windowed Mode, however one can be enabled with the use of registry tweaks. The mode is somewhat limited, it seems the feature was either never completed or perhaps only intended for use during development. Regardless, the game is fully playable in it with only a few graphical compromises.
Enabling
Automatic (LEGO Island Rebuilder)
LEGO Island Rebuilder allows you to modify the "Full Screen" setting on launch without requiring editing registry entries or adminstrator privileges:
Manual (Registry Editing
To enable windowed mode through the registry, you'll need to edit the string value at HKEY_LOCAL_MACHINE\Software\Mindscape\LEGO Island\Full Screen to NO using regedit.
On 64-bit systems, this key will be located at HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Mindscape\LEGO Island instead.
Note that changing settings through CONFIG.EXE will always reset this value to YES, so you'll have to change it back again.
Limitations
While LEGO Island is fully playable in windowed mode, it requires some specific configuration to work properly:
Windowed in hardware mode
Ordinarily, if your graphics mode is set to "Direct3D HAL", LEGO Island will throw a "failed to startup" error. This is actually thrown when the Flip Surfaces setting is enabled, which CONFIG.EXE forces on when "Direct3D HAL" is selected. If you toggle Flip Surfaces off, either in the registry or with LEGO Island Rebuilder, you will be able to run "Direct3D HAL" in windowed mode.
Missing bitmaps
LEGO Island only supports 8-bit and 16-bit color modes, however most modern computers run in 32-bit color. The 3D can render here since it's handled by Direct3D, but the bitmaps are handled manually by the game, and since it doesn't support 32-bit they simply don't render.
This results in backgrounds becoming a solid blue color:
Windows
Starting with Windows XP, applications can be individually set to run at a different bit depth. To do so, right click LEGO Island and click Properties in the context menu. Then switch to the "Compatibility" tab.
Prior to Windows 8, the only available mode is "256 color" mode and your whole system will be temporarily set to this mode until the application quits. LEGO Island will run perfectly fine in 256 color mode, but you may see some color banding or other artifacts.
From Windows 8 onwards, 16-bit mode is also available providing much more color and the mode is only set for the application rather than the whole system. This is strongly recommended for playing LEGO Island windowed.
Alternatively, you can manually set the bit depth yourself to 16-bit in Display properties (pre-Vista) or Screen Resolution (post-Vista).
Wine (Linux/Mac)
The same limitations on Direct3D HAL/Flip Surfaces above apply here.
Wine does not have Windows' 8-bit/16-bit color compatibility mode, nor do their host operating systems Linux and macOS. This makes it difficult to address the missing bitmap/blue background issue.
Instead, it can be better to run the game in full screen, and then enable Wine's "Emulate Virtual Desktop" feature. This will force any full screen game into a window, but also limits anything else you do in that Wine prefix to that window. There are also known graphical glitches that appear for unknown reasons in this mode, though they are not critical enough to be game-breaking.
For a more ideal solution, it's recommended to look into dgVoodoo (see below). You may also need to install DXVK for the game to render correctly.
dgVoodoo
Alternatively, dgVoodoo can force windowed mode if LEGO Island is set to "Direct3D HAL" with full screen enabled. This works on both Windows and Wine and is in many ways superior to the game's built-in windowed mode. It has no limitations on 32-bit color mode and allows (read: requires) hardware mode.
The following images show a dgVoodoo configuration that will force LEGO Island into a windowed mode:
