I run a website that is hosted on a Windows server. I am hoping to shift to a Linux-based server (probably something that runs the cPanel setup, as I am familiar with it).

The biggest issue is that the current website has a static database that is used to serve up information to the visitors. It's the most popular feature of the website, so I want to make sure the transition is right.

This database is an MS Access file. I have a simple ODBC connection to that file, and then I have PHP code that peeks into the file and lets visitors do queries.

My concern is that if I move to Linux / LAMP, I will not be able to make this simple ODBC connection to the MS Access file, and I will need to convert the DB into MySQL. I would like to avoid doing this, as the database comes to me from someone else who operates in MS Access. (I am aware of the possibility of converting to MySQL every time, I just would like to avoid doing so.)

If you can afford to have two systems, one Linux box and another one Windows box, then you can do what you want.

Host your MSAccess file on windows machine and use ODBC to access it.

but what I guess is this will cost you more as compared to one time investment, convert your data from MSAccess to MySql and use it.

I do not know, but there will be a way, you can check source forge for any project if somebody has developed a MS Access support on linux, then your problem will be solved.