Point Scoring based on Rank/Placement

I had a Multi-Event Competition that I'm trying to do the scoring for and I thought this would be pretty straight forward but I'm really struggling. I'll try and explain as best I can....

First, Gray shaded cells identify when a player was disqualified for an event. The reason for two versions of this spreadsheet is because there are events where a player scored 0 points and we have not determined officially whether people who were disqualified should receive no points or a score identical to someone who played and scored nothing but should receive points for being in the bottom bracket (e.g. See the trivia contest where several people didn't answer any questions correctly, but someone was also Disqualified and earns the same rank). So, I want to make two versions to see how this affects the final outcome of the scores.

I don't know how to make the ranks handle the tie scores. If two people tied for first place, Excel skips identifying someone as second place, and instead goes directly to third. I know this is technically accurate because it's ranking them and not sorting them by which place they got. But, in the case of the first event (Long Distance Soccer), it would be nice if Player 1 and Player 2 could easily read that they tied for second place, even though they are both technically ranked third overall.

If Placement (as opposed to rank) is not critical in determining point distribution, I'm fine with leaving the Rank column as it is and not doing some complicated formula to convert it to place values.

For each event, there should be 136 points to distribute between the players.
-- 16 players gives me... "=PLAYERS*(PLAYERS+1)/2"

Any and all help is greatly appreciated. Thanks!

Google Docs Version, but grid lines formatting makes it a little tougher to read.

***Note: I might end up wanting to make three versions of this spreadsheet, where instead of the disqualified individuals having the same points earned as someone who scored 0, I could give them (the disqualified people) a -1 score so that it would create a new rank for them below those who didn't score anything but were not disqualified.