I am deleting the website I originally signed up adsense on, I'll be starting a completely new website and putting my adsense code on there instead. Do I need to contact adsense and tell them I'm deleting the original website?
google wont really care that your site was deleted or not they just care anyone will buy their service or click their ads or not. So you dont have to inform them and hope you do good with your new site.
What they said. You can add a number of websites on your Google Adsense account and Google will just do the rest. However, if your original website gets a lot of traffic, I'm sure you don't have to delete it, you'd get much higher adsense earnings if you put your code on a variety of websites.