First make a copy of the original file and store it somewhere safe. Next please use a hex editor to open the file and see if you can find any public/private key pairs in there. You could then import these into another wallet like Dash Electrum to recover your funds. You can also try to rename the file and open it with Dash Core, but I'm not sure if you will have much luck there. Feel free to send me a private message if you need help with any of this.
1. I installed Dash Electrum, but when I load the file wallet.bin it says "Cannot read the file". What else can I do?
2. I tried to rename the file in Dash Core but it doesn't work.
3. Is there a wallet or exchange that still reads the wallet.bin files?
You've wrote to Dash Service Desk in the past with this issue but there was never any official wallet which were creating wallet.bin file.
If you used Simplewallet then write to the creators of this software.
@datant an OG Dash user has pointed out that you probably mean "Simplewallet", a Cryptonote wallet for Dashcoin. Dashcoin is NOT the same as Dash. I'm not sure if this project is still alive, you could try to open your wallet file using this software instead: https://github.com/forknote/dashcoin