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Welcome to the conumdrums of imaging. You go ISO3200 to make up for the short exposure and you go short exposure to limit the stars becoming eggy. The ISO setting on a DSLR is really a sensitivity booster. It isn't adding anything to the image it is simply amplifying whatever was recorded.
Unfortunately that includes noise. F3.5 for 20 seconds is not going to leave much of a signal. So that leaves maybe 60-90 seconds before you start to really notice the stars going eggy.
ISO1600 may be a better setting and the lowest F ratio your lens will go.
A good lens for this sort of shot is the Nikon 50mm F1.4. Canon no doubt has an equivalent. Not that expensive ($100?) and super fast. You would be amazed at how much brighter your shot would be with just 60 seconds of exposure at ISO1600.
There is also an F1.2 but it may be more expensive
Greg.
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