the data will be there, you should be able to look at the last modified date and it should match about the time the system failed. I have used this method to copy from a development laptop to a production server.
I would install sql to a different directory as well as copy the files to a second location. When I say wipe I mean format so that it starts out fresh, I do that just out of habit when I need to use it as a production server and something happened to it just to be sure it it stable and the previous files cannot cause confusion or problems. It doesn't sound like this is an option so do not worry about it, I just like having things clean. You can probably do a manual clean up after you get everything else back up and running.
fyi: the mdf is the data and the ldf is the log. I would focus my time on backing up the mdf's over the ldfs if space is an issue.