I agree with Phmaximum, you can find some awfully cheap electrics; However, with a budget of $100 you will possibly get a high-end toy grade, or a very very low-end hobby grade car.
I understand the struggle my friend, I own a home, have three kids, 6 cars, and my wife. So I don't have as much time for RC anymore, but I'm managing. I recommend doing what I did, taking a small chunk of your paycheck, 10? 20? $30. A week, however much you feel comfortable with, and setting it aside for savings. It will take some time of course, but instead of wasting $150 on a cheap nitro that is generally pretty slow and will last you what? 2-3 months.
You can save and buy a big name brand, like Traxxas, HPI, Losi, Associated, even Tamiya makes some good cars.
As Phmaximum said electric will be just as fun as nitro without the hassle of cleaning, or refueling. Just recharge some LiPo batteries and you're good to go. From my understanding, some electrics are just as fast, if not faster than nitro cars. I've also heard the Traxxas E-REVO is a pretty good starter car. But don't take too much information from me, I've always been pretty big in Nitro.