The patches supplied in the main .zip for Sacred Gold & Storm Silver are using an outdated format that doesn't work on some systems. Additionally, the original patches target a ROM that is nowadays quite difficult to find.

If such a problem happens, you can try these xDelta patches instead.

The ones labelled "SacredGold105.xdelta" and "StormSilver105.xdelta" are the complete versions of the game with all changes.
The ones that include "Classic" in the filename are modified versions that remove Pokémon changes such as stat, type, level up move and ability changes.

I've included the xdeltaUI.exe and xdelta.exe programs you need to patch them, but if you're on an OS that doesn't support that (such as a Mac), consider using MultiPatch (https://www.romhacking.net/utilities/746/) or the ROM Patcher JS website instead (https://www.marcrobledo.com/RomPatcher.js/).

If using xdeltaUI.exe, remember to include .nds as part of the filename when you select what to save the patched file as, else some emulators such as DraStic may fail to acknowledge it.

The HG/SS ROMs that you apply the patch to should have the following as their CRC32 values. If they don't, the patch may fail to apply.
Heart Gold: C180A0E9
Soul Silver: D8EA6090