You should be able to complete installation without a product code. The option to request a trial license should be offered by the Mathcad License Wizard. If you are being asked for the product code, I suspect, you already installed the product -- it will run in Express mode.
To get a trial license:
Start->Mathcad->Mathcad License Wizard
select "Request a 30-day, full functionality license"
follow instructions. No code is necessary, but you will need to register. If you already registered, use the e-mail you provided as the username.
After you complete the process, start Mathcad and it will indicate you have the trial license.
Hope this helps,
--Jakov