He said it will be fine for him just to have the html processed output, he doesn't care to have it re-written in php.
Where did he say this? It may have been implied in his first post based on his wanting to "convert" ASP to HTML, but the fact that he asked how that could be done demonstrates his lack of understanding of the differences between static and dynamic web pages. It sounds like the owner of the ASP site also shares this lack of understanding, else why would s/he even suggest hosting it on a Linux server?
Furthermore, you made the first reply in this thread, where you offered two suggestions:
You should better have it converted to php if you want to keep it dynamic.
If you just want a static copy, then run in in a localhost iis and save it as html
It's clear from your reply that you did not know whether he wanted the site to be dynamic or static. So again, where did the OP say that he wants only the HTML and does not want the site's dynamic functionality to remain? Did you have some private communication with howard_hughes that is not visible here?
So, if he has the ASP source files, all he has to do is run the website on a localhost supporting ASP (Microsoft IIS).
The OP clearly stated that he "needs" to host the ASP site on his HG plan. If that's the case, then the pages will need to be re-coded as HTML or PHP. If he wants only the HTML and merely changes the file extensions from .asp to .html, then any ASP code in those pages will be displayed in plain text on the web pages and will appear as gibberish to the site's visitors. Also, any of the site's functionality obtained via ASP will be lost/broken.
As for hosting the site on his home PC, that will undoubtedly be more trouble than it's worth. He won't be able to turn the computer off (well, he could, but obviously that would result in the site being down), and he'll need a static IP. There are also security risks involved with hosting a site on a home PC. Let's not forget performance, either: if the site gets a lot of traffic, that could slow the PC to a crawl and/or crash it. Last but not least, ISPs are typically not fond of people hosting websites on their computers.