You can figure a lot of this out for yourself. It is hard to know what you need to do from the information you have given so far.
Each F-Stop (1.4x change in F-number) will let you double the shutter speed and/or reduce the exposure for the same ISO.
Thus if you get the right exposure and shutter speed at ISO3200 at F5.6, then you could shoot at ISO1600 at F4 (one stop below F5.6). You could then say double your shutter speed and go to F2.8 (one stop below F4).
Sometimes even F2.8 is not enough. For my kids basketball, I am often shooting at ISO1600 at F1.8 and am lucky to get the shutter speed to 1/320th.
It would help if you gave what shutter speed at a given ISO you used to give good exposure at a given F-number (basically giving a light reading). Then it can be translate to what a faster lens would let you do.
In dusk conditions under floodlights I have been photographing
sport (soccer) with a Canon 75-300 4-5.6 USM lens and it is not
quick enough to allow a fast shutter speed even at 1600 ISO (whilst
I have 3200 option on Canon 10D noise and 'grain' is too much on
pics). Clearly to move up to a 3.5 or 2.8 zoom or prime lens will
require additional investment which I am prepared to make but I am
after some advice as to how much difference this will actually make
to my being able to photograph in the dusk/floodlit conditions. Any
specific observations on the Canon 35-350 3.5/5.6 in this regard
would be helpful as would any thoughts on other zoom or prime
lenses allowing me to go at least to 200mm telephoto depth. My
preference for a zoom option in relation to sport is obvious but if
my best option is to have a prime 2.8 mid-range telphoto for these
trickier conditions and stick with a slower zoom for other times
I'll obviously weigh up the advice.