Before Serena, Jennifer wasn't a competitor for the GSs, in fact, she started being a candidate probably in the Australian Open 2000 when she reached the semis and lost to Davenport in a contested match.
Australian Open 2000: lost to Davenport, not Serena.
RG 2000: lost to Zuluaga.
Wimbledon 2000, lost to Davenport
US Open 2000: lost to Monica
Australian Open 2001: won
RG 2001: won
Wimbledon 2001: lost to Justine
US Open 2001: lost to Venus
Australian Open 2002: won
RG 2002: lost to Serena
Wimbledon 2002: lost to Mauresmo
US Open 2002: lost to Mauresmo
Australian Open 2003: lost to Weingartner
RG 2003: lost to Petrova
Wimbledon 2003: lost to Serena.
so summarizing, she won 3 GSs, of the others, only lost to Serena twice.
In RG 2002 she would have faced Venus in the final.
In Wimbledon 2003 she would have faced Justine in the semis and if she have won, Venus in the final.
At most she could have two more GSs, but they are very dubious.
If she had been able to win other tournaments, where Serena wasnt there, maybe there would be a point to this discussion. But the fact that Jen has not won a tournament whether Serena has been there or not is your answer. Probably none!