Often this is not the case, especially for low end cards.
The performance of video playback is largely dependent on the video accelerators present.
NVIDIA® PureVideo™ HD Technology: The combination of high-definition
video decode acceleration and post-processing that delivers
unprecedented picture clarity, smooth video, accurate color, and
precise image scaling for movies and video. Feature requires supported
video software. Features may vary by product.
Discrete, Programmable Video Processor: NVIDIA PureVideo is a discrete
programmable processing core in NVIDIA GPUs that provides superb
picture quality and ultra-smooth movies with low CPU utilization and
power.
Hardware Decode Acceleration: Provides ultra-smooth playback of H.264,
VC-1, WMV and MPEG-2 HD and SD movies.
HDCP Capable: Designed to meet the output protection management (HDCP)
and security specifications of the Blu-ray Disc and HD DVD formats,
allowing the playback of encrypted movie content on PCs when connected
to HDCP-compliant displays. Requires other HDCP-compatible components.
Spatial-Temporal De-Interlacing: Sharpens HD and standard definition
interlaced content on progressive displays, delivering a crisp, clear
picture that rivals high-end home-theater systems.
High-Quality Scaling: Enlarges lower resolution movies and videos to
HDTV resolutions, up to 1080i, while maintaining a clear, clean image.
Also provides downscaling of videos, including high-definition, while
preserving image detail.
Inverse Telecine (3:2 & 2:2 Pulldown Correction): Recovers original
film images from films-converted-to-video, providing more accurate
movie playback and superior picture quality.
Bad Edit Correction: When videos are edited after they have been
converted from 24 to 25 or 30 frames, the edits can disrupt the normal
3:2 or 2:2 pulldown cadence. PureVideo uses advanced processing
techniques to detect poor edits, recover the original content, and
display perfect picture detail frame after frame for smooth, natural
looking video.
Noise Reduction: Improves movie image quality by removing unwanted
artifacts.
Edge Enhancement: Sharpens movie images by providing higher contrast
around lines and objects.
This card may support higher resolutions, but can only play back videos of the later formats (which covers most of the ones you want) at 1080p.
Best Answer
Your VGA connection will support HDMI playback. It's a matter of your computer decoding whatever the HD file contains into the correct output display format. HD will depend on if your TV and video card is able to support a resolution at 1080p (or any other HD resolution).
The video card will have to take the data from the player, and display it on the screen. So larger frames in the video will make the video card work harder. Programs like VLC may ask the video card for help too, to decode the HD video container.
Your monitor does not need to have HDMI in order to support 1080p, 1920x1080 is a resolution, DVI and VGA can handle these resolutions as long as your monitor provides it.
VLC contains all the necessary codecs in order to decode HD videos. Your hardware seems sufficient to decode these videos (though it may seem you lack some juice in your hardware). You have a 21'' monitor, depending, it may not support HD resolutions which are 1080 or 720.