No, Adapters only work with Analogue (DVI-A / DVI-I) to Analogue VGA, and Analogue VGA to Analogue DVI-A, they don't work Digital DVI-D to Analogue VGA or vice versa, and they don't use the digital part of DVI-I.
For Analogue VGA to digital DVI-D (the usual monitor input, except for a few DVI-A monitors) then you need a converter box not just an adapter.
You should get something like an ATI 4xxx. You will need a PCIe slot (not AGP).
The newer cards have the advantage of hardware decoders to offload the task from the CPU. For example, a BluRay rip of Hellboy 2 @ 1080p (MKV, AVC) dropped from 65% CPU load using an X2-4800+ AMD to 3% (yep, THREE PERCENT!).
The easiest way to use these hardware decoders is to install K-Lite Codec Pack (Standard or Full). Use the included Windows Media Player Classic Home Cinema (WMPC-HC); you need to enable DXVA in setup or after in the Options.
Again, look for a newer card that has H.264/AVC, VC-1 and MPEG2 hardware decoding (aka "UVD").
This dependson the following:
2) Power Supply
3) Purpose (gaming?)
For example, an X2-4800+ CPU can use up to about an HD4850 at which point most games are limited by the CPU.
All modern cards are pretty much identical for Windows multi-tasking. It only really matters for gaming (and connectivity such as HDMI).
I thought I'd add that the DVI output actually has TWO outputs on it. It has the pins for DVI (digital) and it has the pins for VGA (analog). The VGA "adapter" is simply hooking up to the analog pins only. The DVI cord does the reverse, it hooks up to only the DVI pins and not the VGA ones.
The VGA signal out the output of modern video cards is created by tapping off of the DVI signal, sending it to an D/A (Digital to Analogue) chip then out the pins. At the monitor, the VGA is then converted BACK to digital via an A/D chip.
Just FYI. It makes little viewable difference in reality, though it's best to stay DVI all the way if possible.
I am thinking of swapping out the radeon 4650 on my new pc i bought from HP and putting it in my old pc which i will be hooking up to the tv for streaming movies since it had a dvi output. I can then but a 4850 and use it for my new HP. The problem is that i dont know if it will void my warranty, considering i just purchased it. I will be using my new pc for gaming and i have a 1920x1200 24" lcd.
I decided that I will just keep the video card in my new PC and just upgrade the one on my old PC so that I can use it with my TV. What is the best video card for $75 or under for watching streaming movies?