Check your option codes on the sticker under the hood, and match them up with something like
https://www.stuttcars.com/technical/option-codes/986-00-02/ , should be able to tell if you had it originally. Look in the 510-540 range, the options are there I think.
Mine is a '97 that didn't have an alarm or keyless entry, and had a key like yours with just the light on it. I added them both very simply and cheaply following this thread:
http://986forum.com/forums/diy-project-guides/56773-3rd-party-keyless-entry-diy-why-not.html