What is the blinking light on the back of my PC tower?
For about the last 5-6 days, there has been a bubble pop up from the toolbar and it tells me that a local area cable is unplugged. It pops up and then goes away and then pops up and goes away etc., etc. I have also been having problems with my internet connection. My modem and router are working fine, since I am writing this using my wireless laptop. Is the blinking light my ethernet card and do I need to replace it?

Blinking light is probably the activity light on your ethernet card and it’s normal for it to blink.
If you get a bubble coming up saying it’s unplugged, plugged in, unplugged etc then the cable could be loose or need replacing…or like you said the card could need replacing but that should be the last option….try the cable first
the blinking light at the back of your PC is your LAN card. it should have two, yellow and green (i think)
if you are having problems connecting through the internet, your ethernet connection is probably loose. apparently, your modem and router is working properly. try checking your connection first before spending money on a new LAN card. its probably loose since you can connect sometimes.
or you can try updating/reinstalling the driver for your LAN card
Check your ethernet cable on both ends. Make sure it is plugged in securely. If your computer keeps indicating the cable is unplugging a lot, you could have a pinched or broken wire in the ethernet cable. Try to replace it. I would replace the cable before the card. If it was the card iteself, you would see different kinds of errors.
The cable has a bad connection.
Try pushing i all the way until you hear a click.
But if its loose, you may need to replace the terminals at both ends.
If its too difficult for you, buy a new network cable at your nearest computer store.
The blinking light on the back of your pc indicates that your cable is sending signal from your modem to your ethernet card. Try checking the cable for any breaks or fringes. If there is none then try unplugging and then replugging it back. If none of those work then you will probably need to either replace the cable or ethernet card.