Ranking Without Skipping, combined with IF conditions

Hi guys and gals,

First, this site has helped me a lot over the years, and I now regret not signing up sooner so I could give reputation to users who have helped. But thank you all in advance.

I'm trying to assign ranks by point values in another column. I do not want tied ranks to cause a skip in the ranks (i.e. going from two people tied in rank 4 then going straight to rank 6). However, I also need to implement my IF function to only apply the ranking if there is a name entered in Column A, as the number of participants fluctuates frequently. I have tried several variations of formulas and haven't been able to make any of them work. Any help is greatly appreciated.

I have simplified my spreadsheet into this sample file with a few of the attempts to show the results.

In the original form, I get tied values and skipped ranks using the formula:
=IF($A3<>"",RANK(C3, C$3:C$14, 0),"")
Sample.PNG

In Sample 1, I get a #DIV/0! error using the formula:
=IF($A18<>"",(SUMPRODUCT((C18<C$18:C$29)/COUNTIF(C$18:C$29,C$18:C$29))+1),"")
Sample1.PNG

In Sample 2, I get all rankings as #1 using the formula:
=IF($A33<>"",(SUM(IF(C33>C$33:C$44,1/COUNTIF(C$33:C$44,C$33:C$44)))+1),"")
Sample2.PNG

And in Sample 3, I get a completely incorrect ranking with decimals using the formula:
=IF($A48<>"",(SUMPRODUCT((C48<C$48:C$59)/IF($A48<>"",COUNTIF(C$48:C$59,C$48:C$59),""))+1),"")
Sample3.PNG

All suggestions are greatly appreciated.
(PS: There will ultimately be 7 rank columns being summed and ranked again, and will need to use one of the rank columns as the tie-breaker, if that will matter)