Greg,
regarding the former "Electorate of Hesse" see i. e. here:
https://en.wikipedia.org/wiki/Electorate_of_Hesse
Scroll down on this web site and enlarge the map on the right titled "Kurfürstentum Hessen" in order to get an impression how huge that territory was.
I mention this since if you indeed only have a name and for place of origin "Hesse-Kassel", then looking for her comes close to looking for a needle in the haystack - not impossible to find the desired person, however a really tedious task.
Anyway, the "Landeskirchliches Archiv Kassel" (regional state archive Kassel) has 1,819
microfilmed church books in their holdings - see here:
http://www.archiv-ekkw.findbuch.net/php/main.php?ar_id=3690#4b42204b617373656c
Click on "Liste der Verzeichnungseinheiten des Bestandes Verfilmung KB Kassel" in order to see the details.
Quite a number of these are already digitalized, but not everything as of yet.
If you want to wait with starting your research until allmost everything has been digitalized and will eventually be made available for online-research via Archion I'd say that you may have to wait for at least the next 1 1/2 up to 2 years or even more to come.
Back to Archion:
...as a general rule: online available church books appear on Archion on
GREEN background.
Everyone can see what is online free of charge and even free of any registration at Archion.
In your case....
Browse > Landeskirchliches Archiv Kassel
next column to the right is the church district > click on any
next column to the right is the parish > click on any
next column to the right shows the available church books for a parish
If you actually want to access any of such available church books (appearing on green background), as a registered user of Archion you first need to buy what they call a "Pass / Passport" - say a paid subscription.
Hope that already helps a little and good luck with your research,
Vera (Nagel)
PS: Since church book records are recorded in historic German script one needs to be able to decipher these scripts. In case one runs into difficulties doing so, the Archion forum has a sub-forum titled "Lesehilfen" (deciphering help) where Archion users may ask for help free of charge.