Installing MySQL on server for self hosted domain

Forgive my ignorance.

Im trying to install wordpress on one of my client’s websites, but the domain is self-hosted, and does not have MySQL.

This client also has almost no technical knowledge and there is some unknown issue getting their usual tech support to do this.

I need to know how i go about installing MySQL (and probably PHP MyAdmin) on their server.

The currently the server is using a microsoft SQL installation with ASP in the website - THIS CANNOT BE INTERFERED WITH.

The client needs their ASP and Microsoft SQL functionality to remain intact. They have INSITE and OASIS systems that are necessary for their buisness.

Also the ASP functions have been integrated into the WordPress website i built them. (i built the site on my testing domain with the intent of transferring everything once it was complete).

That said I need to install this WordPress website on their server and WP only works with MySQL.

Im not at all experienced with these things. im just a small time web coder.
The only experience ive had directly with SQL is changing the URLS in the database so i could transfer a WP installation from one domain to another.
that was a simple mater of Find and Replace in Dreamweaver. I have ZERO understanding of SQL languages.

i have no idea at this time whether the server is running apache or iis.