tl;dr: Just don't.
You cannot learn to play music by using your computer keyboard. It's like trying to learn cooking using an excavator. Or to drive a car with your chin.
What you're experiencing is due to the rollover limitation of common computer keyboards: they can handle only few keys pressed together. It's not just a matter of the number of pressed keys, but their position in the keyboard matrix: except from modifier keys (like Ctrl or Alt), there are only many (close) keys that can be kept pressed and correctly recognized as such at the same time, and the order of press events also matters.
Consumer keyboards usually can get up to 2-4 keys at maximum, depending on their position: the more they're close, the less you can press together.
There are some high-end "n-key rollover" keyboards, usually aimed for gamers, but their price is usually high (80-100$ at least), which makes it even more useless for this matter: playing with a computer keyboard (especially if using alphabetic notation) has really very limited benefits - if any. Besides the above problem, computer keyboards have layouts that don't follow "musical" requirements, so in the end trying to play with them is just uncomfortable, pointless and with great limitations.
I strongly suggest you to buy an actual keyboard: even a cheap and small one would be hundreds times better (for example, the M-Audio Keystation Mini).
You may not be used to that (and then believe that using your laptop's keyboard is better), but it's just a matter of habit, and in the long run (actually, not that long) you'll only see benefits.