Here's one easy way to get your leading zero back.
Step 1: Create an on-demand workflow (or ask your system administrator to do it for you). The Zip code field is probably listed down towards the bottom of the page. Type in a "0" (that's what the red arrow is pointing to) in the field then, using the controls on the right, set the field to the zip code field:
Step 2: Create an Advanced Find query to get a list of all your Accounts with this issue; that is Accounts from the states whose zip codes start with zero that have zip codes that don't begin with "0". Don't forget to save this View!
Step 3. After clicking the Results button, Select the Accounts and click Run Workflow.
Step 4. Select the Workflow created in step 1.
After the workflow has successfully run, this view will be empty. Once you have your workflow and your Advanced Find View created, finding and fixing zip codes with a missing lead "0" is easy and takes less than a minute.