Ask HN: How would you get a tech internship in high school?

Without any concrete proof of technical skill, it's hard to prove to a company that they should take me on as an intern, especially when there is a low chance of me returning to the job immediately. My resume is actually pretty strong - I have some quantifiable work experience with Linux and website management (2 separate projects) but no useful JOB experience. In addition I live in an area with access to a large tech center that has a lot of interesting software and hardware companies.

How would you go about applying to these companies? I already understand hiring basics like how to construct a resume, cover letter, interview procedures etc... but I'm wondering what I can do to increase the chances of getting a real call back from tech companies.

What companies would you apply to? My guess is that monolithic companies with complex hiring and internship tracks won't want to deal with an oddity like my application, so I have been targeting small teams that are more agile as well as medium-sized companies with distinct teams. Is this a good plan? Should I just apply everywhere?

If you were reading applications at a tech company, what would make you consider a high school student?