Hi powka!
You need to get a copy of your wallet.dat file. Store it in a couple of places to keep it safe, just in case you make a mistake. Then install the latest version of Dash, start it once, close it, then copy the wallet file into the DashCore folder.
Full instructions here:
If you have the old program, then you have the .dat file on your system. I don't know if you are on macOS/Windows/Linux, but it should be in the application data folder described in that documentation link I sent you, e.g. "%APPDATA%/Darkcoin" folder under Windows. You can also find it by going to "Tools -> Show Automatic Backups" and then go up one folder level. All your blockchain and wallet.dat files should be in there. Shut down the Darkcoin wallet and make a backup before you try and restore it, good luck!
If the program is able to start and display your balance, then I believe your wallet file must exist somewhere.... If you start it without an existing wallet file, it will usually create a new file and display a zero balance.