First thing you will need to do is download Cheat Engine from this link http://www.cheatengine.org/downloads.php
You must also have Silent Hill 4: The Room already installed.
First, start up Silent Hill 4 (You do not have to be in game, this can be done from the main menu as well)
After making sure that it is currently outputting a resolution of 640 x 480 (default) minimize it and open up Cheat Engine
Select the SILENT HILL 4.exe process from the top left button and type the width value (640 in this case) into the text box and click the First Scan Button, this will list many variables containing the number 640, two of them represent your width. We can separate these two by changing the game's resolution to 1024x768 from the in-game menu like below.
After you have done this, type 1024 in the text box of Cheat Engine and click Next Search, this will highlight two variables in green, double-click them both so that they appear in the bottom list.
Change the value of the two variables to your screen's width (in my case 1366) and then re-open the game. The game's resolution should now match your screen's.*
NOTE: This method results in a Stretch type of widescreen display, meaning that the FOV is unchanged.
*If your resolution height is NOT 768 then you must repeat the process for the game's height
