How do I upgrade from 2.4.1. to 2.4.4 and keep original data

I built which uses 2.4.1 -- Someone else has taken over as the web master and the site was was hacked and now doesn't function properly. Now the people I built the site for have come back to me to fix it. I would like to update it to 2.4.4. but want to keep the original databases which I believe are okay. Are there any specifics I need to know as my client doesn't want to lose the original data.
thanks

Back up existing files.
Download latest version.
Extract latest version.
Delete config.inc.php from latest version.
Upload new files to replace old files.

Thanks Carbonize, but it isn't working properly yet.

1. The capcha doesn't seem to be working, so the form isn't updating. I don't see any of the capcha code at all.

2 The original site had the site header and navigation wrapped around the code, so it displayed with the site name and nav buttons above the guestbook. I am not sure how to include that back in.
thanks,

not sure if you have to visit misc/db_update.php or whatever the file is called.

2 - Should be able to put your old header and footer files in the templates folder.

Where is the misc/db_upade.php? On the guestbook site or somewhere in the update? The problem with the header and footer is that the new website designer has changed the structure from my original. Once I get the capcha working, I will have him deal with conforming it to the rest of the site.
thanks.

In the guestbook folder is a folder called misc. In that folder is a file called either db_update or update_db and you need to visit it in your web browser. It's either that or there is something new in the config.inc.php file of the newer version so you will need to copy your information from the old one to the new one.

I had actually found the db_ubgrade.php in the misc. directory and ran it. It told me I was okay. So, I guess I will compare the 2 config files and see what might be new and missing. I'll keep you posted.

In looking over the files, it is not the config.inc.php. They are identical except for the specifics for the site, like database name etc.

Message me the link to your gustbook so I can look at the captcha.