What statistical method can be applied in my case? I want to study the impact of 26 parameters on one variable, and therefore determine the 3 or 4 which have to most influence on it. For that, I have constructed a 10 x 26 matrix: 26 parameters with 10 observations, and a vector of 10 arrays containing the variable I want to study with 10 observations. From this, how can I determine which are the 3 or 4 most influential variables on the parameters. I was considering using PCA, but I'm not sure that's the right approach. Can anyone give me some direction here?
There are a number of methods for this. Here's a list:


You can build a Regression model and observe the p-values of the coefficients of each variable.
Pearson Correlation
Spearman Correlation
Kendall Correlation
Mutual Information
RReliefF algorithm
Decision trees
Principal Component Analysis (which you have tried)


etc. 

You can search for other methods with these keywords:

feature selection, variable importance, variable ranking, parameter selection

They are all almost the same, just different terminology in different fields.

However, the issue that you MUST pay attention here is "10" observations are almost nothing. It will be extremely difficult to trust any outcome, regardless of the method you use.