There's a distinction between individual items like your photos, videos, music files and the individual text messages. Things like photos are their own actual file, but text message files don't get stored as individual files, they get added/deleted into a mini-database file. This also applies with email messages so with individual email and text messages, you need to try to access the email database file and the text message database file, then use something like a text editor to read the messages within those two files.
Since you've purchased a USB cable for this phone, if directly viewing this phone's internal storage is a problem using a computer's default file manager, you might want try using this BitPim utility:
http://www.bitpim.org/
https://en.wikipedia.org/wiki/BitPim
Keep in mind that remotely accessing the file system on a 12 year old phone could be something of a real project.