Hi Laura and welcome to FixYa!
Yes, you should be able to change your monitor. You will notice that if you unplug your monitor's cable from the back of your computer, you will see an adapter that looks like the one below (called VGA).
I can't seem to find the specs on the new monitor you mentioned, but most new LCDs (flat screens) have DVI cables, which look like the picture below.
Don't worry, its an easy fix. Go down to your local electronic store and ask for a "VGA to DVI converter". It will look like the one in the picture below. Mine cost me about $8 USD.
I hope this helps. If you have any questions, do not hesitate to ask.
Happy Holidays,
-TJ