I've been using the laptop since Christmas with no problems at all, then suddenly, one day it stopped working. Any attempts to connect to the internet using dial-up result in a "No dial tone" Error. According to the device manager, the modem is working correctly. The troubleshooter was unable to solve my problem. It's not because of my phone lines or anything, I'm connected on the same phone jack on a different computer. Tried contacting my internet provider, no help at all.

Anyone experience anything like this before?

Luckily the modem card is replacable. Modems fail easily and quickly if you are living anywhere that lightning storms are present. You will get small voltage, invisible lightning coming down the phone lines that comes down the phone lines. Phones are tough enough to handle it, but laptop modems are not.
The symptoms of lightning or electrical damage (it doesn't take much) are what you describe. Of course you would want to try a different modem first, if you could, before you buy one. So try the bench where you bought it, or a friend with a similar one... you can determine exactly which it is by running the free Belarc Advisor or the free Everest.

Alright, I was expecting I would have to buy a new modem anyway. You wouldn't happen to know if its easy to install a new modem on a laptop, would you? Like would I just have to unscrew a plate on the bottom and take out the modem and put in the new one, or should I have a professional install it?

On most Toshibas, there is a little removable plate on the bottom, about 2 X 2 1/2 with one screw holding it on. Inside there is a bag of hardware in a little envelope of thick soft plastic... with wires sticking out. Sometimes the wires plug into the other wires. Sometimes they most be soldered. Everything you need to know about model is printed on the bag.

Okay, thank you very much.

you can remove the modem card and check the contacts soldering of the modem card and on mb modem connector. i'm sure, that there's bad contacts soldering.

The common fix is to stuff a folded business card between the device and the
cover plate! It's a bad connection and the extra pressure has proven effective
for others.