It's not the number that matters but the quality. So if they are quality then you have a good chance but if not then they probably will not help you much.
A good link is from a site in the same niche as yours. Focus on quality of link, not quantity. 1 link from a related site (that also has quality content) is much better than, say 20 links from unrelated sites.
Only Google will decide which links are of more quality then others Get backlinks from sites related to your niche.
Google toolbar can determine the PR of a particular link which may help you to choose which back links to go for.
it is really depends. it your 2000 backlinks is all quality then you can have an oppurtunity to rank high. still content is king
Its the quality of back links not the number of back links. Google gives more value on the quality compared to those irrelevant sites that you are getting.