No bitcoins in my multibit wallet, but I have some when I look in the blockchain
I just deleted my original answer now because I realised it was wrong.

If you have a wallet.dat file, then multibit classic is not the Bitcoin wallet you would have used. Chances are, you used the original Bitcoin software.

First you will need Python 2.7:
64 bit version
https://www.python.org/ftp/python/2.7/python-2.7.amd64.msi

Download this private key extraction utility which will display the private keys for your wallet.dat

https://github.com/dlitz/pywallet

Download the zip and unzip.

Open the command line (windows key + r) type cmd then press enter. Change directory to the folder you downloaded ie:

cd c:\Downloads\pywallet-master

Or c:\users\mike\downloads\pywallet-master

then type:

python pywallet.py --dumpwallet

press enter and you should hopefully see a list of bitcoin addresses and private keys (which start with the number 5).

Once you have these private keys, open a wallet with blockchain.info

and once you're in, click on the Import/Export button and click 'Yes I know what I'm doing'.

Click on Import wallet in the left side column.

You can then add the private keys by copying and pasting the output from the command line.