The thing to get your head around is what happens on the server, and what happens in the browser. An ASP page is executed on the server, then the resulting HTML is sent to the browser. There is no connection from the HTML page to the ASP or recordset on the server, ASP just generates the raw HTML and sends it to the browser.
Once the HTML is sent the recordset no longer exists, and even if it did exist the browser can't connect to it because it's on the server and there's no connection from browser to server. ASP just generates and sends "normal" HTML pages.
So, to populate the full VIN text box with a partial value entered in a HTML form, you must send the partial value to an ASP page on the server, which then queries the database and sends the full VIN in the HTML it returns.
There's two ways of doing this:
1. Easiest way: user enters partial VIN, clicks "Get Full VIN" button that submits to the server ASP, which then looks up the full VIN, and returns the same page but now with the looked up full VIN in the <input value="here">.
You could do this as two pages: first page for just partial VIN input and "Get Full VIN" button, which submits to a second page with the full VIN and all the other inputs.