I can't hold down fire and move down/left at the same time.
What AM said. This is a rollover problem, your keyboard only has small amount of keys it'll register as "pressed" simultaneously. You usually don't see this issue much with external keyboards ('though I have a Saitek Eclipse that has about a 3-key rollover), laptops are hit or miss. The keyboard on my expensive Asus "gaming" laptop has only maybe a 2-3 key rollover, depending on the keys (including the same fire+down+left problem).
So yeah, either get a good USB keyboard (check it's rollover before you buy), or a controller.