Gday stefanie,
Now by all means I am no pro here, but I'm going to go out on a limb, I'm sure I will be corrected swiftly if I am wrong

The lock you have is a
Lever Lock of some sort. In theory, all lever locks should actually have some levers in them to match the key, but looking at your picture, there dosent appear to be a lot of room for them, so it may not. This is / was suprisingly common on cheaper locks, and means that you only need to throw the bolt, rather than actually pick anything. I would make a tool out of coathanger wire that was 'L' shaped like the key would have been, with the end of the 'L' the same size as the lock hole. Insert you new key / bolt-thrower and try turning it, making sure that the entire L end is inside the metal part of the lock.
Your 'key' should look something like one of these.

See how you go with the above, if you don't have any success, the lock may indeed have some levers and require to be picked. If thats the case, the best thing you can do is take it to your local locksmith for opening, lest you damage the lock further.
Best of luck,
adi_picker