Cheaper than $35?
For that kind of price it's pointless to get 256 MB of video memory. The rest of the card will be far too slow to utilize applications that can efficiently use that much memory.
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Well you asked for the cheapest yet still functioning card I could find, and here it is.
Personally I despise the FX series but...
HERE
It'll do web browsing, office stuff, pictures, probably video streaming but not at high resolutions, and a few low-end games. If you don't plan on gaming or streaming hd video on this pc then this card *should* do the trick.
Specs:
Fan: No
Core: 250MHz
Memory clock: 300MHz
VRAM: 128MB
Interface: 64-bit
Pipelines: 4
Dx: 9
$27 off of Newegg.
AGP 4/8X Slot
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Is this one closer to what you were looking for?
Also, the details mentioned above (my first post) would be extremely useful in helping me find you an appropriate card.