Yes it would appear your imagemagick does not support png files. You need to totally recompile imagemagick and the necessary libraries to use imagemagick otherwise stick with GD2
As long as there are no errors you should be okay on compile but those instructions essentially come from Imagemagick site since your dealing with their server software and its installation. If things work with GD2 then there has to be an issue compiling Imagemagick with PNG support on that server. You can see when running the configure command via ssh scan back when its done and see what support was enabled.
ImageMagick is configured as follows. Please verify that this configuration
matches your expectations.
Host system type : i686-redhat-linux-gnu
Option Value
-------------------------------------------------------------------------
Shared libraries --enable-shared=yes yes
Static libraries --enable-static=no no
Module support --with-modules=no no
GNU ld --with-gnu-ld=yes yes
Quantum depth --with-quantum-depth=16 16
Delegate Configuration:
BZLIB --with-bzlib=yes yes
DPS --with-dps=yes yes
FlashPIX --with-fpx=no no
FreeType 2.0 --with-ttf=yes yes
GhostPCL None pcl6 (unknown)
Ghostscript None gs (unknown)
Ghostscript fonts --with-gs-font-dir=default none
Ghostscript lib --with-gslib=no no
Graphviz --with-dot=yes no
JBIG --with-jbig=yes no
JPEG v1 --with-jpeg=yes yes
JPEG-2000 --with-jp2=yes no
LCMS --with-lcms=yes no
Magick++ --with-magick-plus-plus=yes yes
PERL --with-perl=no no PNG --with-png=yes yes
TIFF --with-tiff=yes yes
Windows fonts --with-windows-font-dir= none
WMF --with-wmf=yes no
X11 --with-x= yes
XML --with-xml=yes yes
ZLIB --with-zlib=yes yes