Our new Epson Stylus TX110 used up the initial introductory black ink cartridge. Upon replacing it with an authentic Epson ink cartridge, the printer keeps saying it is empty of black ink and will not print.

Check these FAQS:
Replacing Ink Cartridges

You can also find a HTML user's guie for your printer here:
http://support2.epson.net/manuals/english/spc/stylustx110tx111/guide/index.htm

check for the driver
& start the clean setup for ur printer

click on the printer tab in start menu or control panel.
Right click on your printer and click on preferences, click on the advanced tab and click on ink cartridge replacement

If you are using non-Epson nink cartridges you may need to get a replacement set of cartridges. Secondly, the ink sponge could be full. You can try a soft cloth to remove the excessive ink. Also, take a look here for the Epson utility to correct your error. Please leave positive feedback . http://www.ssclg.com/epsone.shtml

why dont try with a new black cartridge. may be the cartridge is falty.

You should be able to refill the cartridges with no problem I do it all the time on a variety of different printers, I'm not familiar with that particular model, I am guessing that you are in Australia, here is a quote from their page for your printer:
"This printer is designed to be used only with Genuine Epson Intellidge™ ink cartridges
Intellidge™ Ink cartridges are not designed for refill."

So I am really not sure hope that has been some help.

If this helps, with the Epson C40 Stylus here in Canada there is only two cartridges black and one for the the colors if you rub your over the sticker if there is one towards the back of the cartridge it should show an indentation this is on the C40 cartridges, this is where you fill the cartridge, same on the black I believe, that or may not work for you.

ink pad end? end life? Reset waste ink counter using epson tx110 resetter.

The procedure is shown on the panel you can see if you open the cartridge compartment of your TX110. However, it can take some effort to decipher the icons. It is known to work if the ink low light is on, untested otherwise.

1. Turn on the printer.
2. Press and hold the STOP button until the cartridge tray moves out of its bay. It will stop at the ink low notch pointing to the first cartridge out.
3. Press STOP again. The cartridge tray will move to show you the next cartridge low on ink.
4. Repeat until you know all cartridges out. After the last cartridge pointed to, the tray will move again and stop in the area where all cartridges can be accessed by hand.

That's it folks!

i have resetter on epson tx110

Did you change from matte black to photo black? Or vice versa? If so you have to use the ink conversion kit that came with your printer and draw out the old ink and install the new black in cartridge. Try page 113 in your owners manual. I am having a similar problem but with the light cyan and it says "set ink cartridge".