Read through a log file to find "Fail" lines
The standard indentation for Python, specified by PEP 8, is four spaces.  This is a pretty strong convention for Python, since indentation matters a lot.

You almost always want to call open() in the context of a with-block, so that the file will get closed automatically when exiting the block.

This task does not require you to read the entire file at once.  I recommend working line by line so that you can handle large files better.  (You also don't need to make a copy of myResList at the end using myResList[:].)

You don't need a regular expression to search for a fixed literal string.  A substring search will do just fine.  This also means that your function is misnamed.  In general, you should name functions after the task that they accomplish, rather than how they accomplish the task.

I'd generalize your function to search for any text.

def search(filename, text):
    with open(filename) as f:
        for line in f:
            if text in line:
                print(line)

if __name__ == '__main__':
    search('/home/nick/python/chap8ReadingWritingFiles/15Jan2016_000000.txt', 'Fail')


If you're interested more in passing back the results, a better way would be to yield the results back to the caller.

def search(filename, text):
    with open(filename) as f:
        for line in f:
            if text in line:
                yield line

if __name__ == '__main__':
    for result in search('/home/nick/python/chap8ReadingWritingFiles/15Jan2016_000000.txt', 'Fail'):
        print(result)


The if __name__ == '__main__': boilerplate is optional, but considered standard practice.