from 2000-2004 the Williams were running the show and Lindsay was sort of fighting Henin, Clijsters, and a few others for best of the rest.
That accessment is very generous to the sisters, and extending it to 2004 is enormously kind on your part. 2002 is obvious, and the only year I entirely agree with. First of all in 2004 the sisters were not running anything.
Serena's slam results in 2004- quarters, final, quarters
Venu's slam results in 2004- 3rd round, quarters, 3rd round, 4th round
There were probably 7 players that had better years than Serena in 2004- Henin, Myskina, Kuznetsova, Mauresmo, Davenport, Sharapova, Dementieva. There were probably all those plus Serena, plus a few others, who all had better years than Venus who was close to irrelevant that year. So at the very least cut that span down to 2000-2003. In additions to the fact they were far from the 2 players to beat in 2004, Venus and Serena were a combined 0-5 vs Lindsay in 2004 as well so they were irrelevant to her lack of success that year. That year her problems were Henin (when healthy), Clijsters (when healthy), the emerging Russians, and her own constant choking/bad luck pointed out before.
In 2000 and 2001 Venus most acknowledged as the #1 player that year, not in official ranking but in practical terms. However Serena was certainly not the #2 either year. In 2000 Hingis and Davenport both had a 1-1 head to head vs Serena, but far more success in the slams and overall. In 2001 Capriati was 3-1 head to head vs Serena, plus had more successful overall results, so Serena in no shape or form was over her that year. I would put Serena over Hingis and Davenport in 2001 personally because of all her tier 1 titles that year (Indian Wells, Canada, year end Championships). Serena was really #4 in 2000 and #3 in 2001.
In 2003 Serena and Henin were the 2 top players really, not Venus. Both won 2 majors of course. Venus and Serena both had to miss the U.S Open by injury, but Justine was not the same Justine by then as she was in Australia when she lost to Venus in the semis. Venus also was injured and very subpar at Wimbledon but was lucky Clijsters choked in the semis, and Serena took pity on her ailing and struggling sister to let the final go 3 sets. I have little doubt Justine would have beaten Venus in the final or semis there had the played, despite that she was stomped by a blazing Serena in the semis.
Then again if you are talking about atleast 1 being dominant than 2000-2003 would still be a fair period. Definitely not 2004 though. The sisters have ruled in the last year about 7x more than they did in 2004.