Almost always you will want #1, because almost always you will be talking about an event that has already happened -- even if it "just" happened. As a standalone sentence, #2 is unusual. It might be used in a historical-present narrative, but that's about all I can think of.
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lokon1)I almost started a fight ( with a driver on the way home yesterday ).
lokon2)I almost start a fight. - Nothing wrong grammatically, but present tense in this context doesn't sound right to me.