Non-parametric repeated measures guidance needed

What I am studdying is Aspergillosis (a disease) -it is caused by the terrestrial soil fungus called Aspergillus sydowii - of the sea fan Gorgonia ventalina.

What I know so far:

1) My data is non-parametric....Residuals are not normally distributed and transformations do not help.

2) I Ihave repeated measures (sampling - ~440 sea fans total- through time).

First: I hypothesize that the prevalence -among other things- of the disease will differ throught time (seasonality) and space (sites).

Second: The differences in disease prevalence in space and time can be attributed to other variables that are also measured....Including: neighboring watershed use, rainfall, marine temperature, wave height, marine nutrient loads, and sediment loads entering the bays- sediment is broken into organic, carbonate and teriggenous fractions)

My data comes from 4 sites (4 different bays)

Within each bay there are 4 quandrats (repetiotion within site) with ~ 25 sea fans in each. Each sea fan has its own ID#.

All sites (all fans at each site when not "missing") were sampled 10 times over the period of one year (repeated measures/ repetition through time)

The breakdown of data above is for any data collected on sea fans----really what I need to do at the very least is determine if and where there were differences in disease prevalence by site and time.

Below is information about the other variables.

I realy would like to figure out some way to assocate these variables with disease prevalence. For example: more rainfall and or more land development leads to more runoff (in the rainy season) which results in more sediment and nutrients whic results in more disease....or something like that....but there are no clear direct trends in the graphical results.

Sediment Data was collected using sediment traps. There were 3 traps in each bay. Sedment traps were swapped with each sea fan survey. This means I have repetiotion within site (3 traps) and through time (9 collections of traps coresponding with surveys 2-10 of sea fans)

HOBO temperature loggers were left out for the durration of the field surveys (one at each site) So no repetition withing site to get a standard error between loggers....... but the sampling rate gave me a standard error for temperature over the given sample period for the one logger at each site.

One sample for dissolved nutrients and one sample for total nutrients was collected from each site, each sea fan survey. So no repetition withing site to get a standard error.

Wave data comes from one buoy for all 4 sites through time ( I broke wave data down by site and sample period to get the mean significan wave height for each site over the actual period of time between each site being sampled ) Again no repetition withing site to get a standard error, but the sampling rate of the buoy allowed for a standard error over the sample period.

Rainfall data was collected using 3 Davis Weather stations spread across the island in a way that they were assocated with 3 of the 4 watersheds.

What I am thinking is that for comparing one site to itself through time I would use a Friedmans rank test.
To compare all 4 sites at one time period I would use a Kruskal Wallis Test

.....but neither test incorperates my other variables----my stuff is multivariate with the dependent variable being disease prevalence or some factor regarding the sea fans...Is there some test where you can have 4 sites and 10 time periods and mutliple variables????

Also, if I use Friedmans rank and I find there is a an effect of time at a given site what follow up test do I use to determine where that difference is?? I want to have connecting lettter reports with my graphs.....I was thinking Wilcoxon signed rank test but that is only when you are comparing 2 groups group it would be time period of which I have 10.....Here I get even more confused.

I am using JMP to run stats.
I could also use PRIMER.
I do not know R or SPSS :(