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system is computationally singular: reciprocal condition number

I know, this is a fairly common question and I am really disappointed that I could not find a solution.
I am trying to calculate Mahalanobis distances in a data frame, where I have several hundreds groups and several hundreds of variables.

Whatever I do, however I subset it I get the "system is computationally singular: reciprocal condition number" error.
I know what it means and I know what should be the problem, but there is no way this is a singular matrix.

I have uploaded the input file to my ftp:
It is a tab delimited txt file with no headers.

I was working with the StatMatch Mahalanobis function.
I have a deadline for this project (not a homework:)), and I could always use this funct, so I thought I will be able to quit the calculations short, but now I am just lost.

I would really appreciate any help.

Thanks for any help