Note: In the original question I was in a hurry and wrongly assumed that the problem was related to VCL Styles, but at the end after some testing it seems to be related to the SynGdiPlus.pas, so I removed the original description.
The problem:
TImage correctly shows the image at designtime but not at runtime.
The cause:
Gdip.RegisterPictures;//initialize SynGdiPlus.pas from Synopse.info
My solution:
Removed the use of SynGdiPlus.pas and notified the author about the problem, use the built-in support for PNG files provided by VCL.
Your version of SynGdiPlus is clearly deprecated.
The current revision has a NOTSYNPICTUREREGISTER condition, which is enabled by default:
initialization
{$ifndef NOTSYNPICTUREREGISTER}
Gdip.RegisterPictures; // will initialize the Gdip library if necessary
{$endif}
Ensure you got the latest revision of the source code tree.