"Integrated security" is probably your problem, if the DB is still on the same PC as it was - the user on the "new" machine probably isn't authorised to access your computer.
You shouldn't really use integrate security in production anyway - using SQL authentication allows you to select an SQL user (which is not the same as a PC user) that has just sufficient privileges to do the job your app needs, and no more - which can help to protect your DB.
Have a look here:
Simple SQL Connection String Creation[
^] - it may help you generate a string that will work.
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