If you haven't found a drain pipe, stop looking, there isn't one. If you did, that might present even more problems as it would indicate a clogged drain or worse...like a non-functioning drywell.
The problems occurred during a rainstorm, right? On the 2 ocassions you noted when water came into the basement, was there a torrential downpour beyond what you normally see, or was it normal rain?
How old is the house? How long have the window wells sat unattended (like anyone really cleans them out, right?). If the house is 30 years or more old, chances are the wells haven't been cleaned. Most often, when the wells have problems draining, it's because there isn't free draining material under them, or the voids in the pea or crushed stone fill have been filled with silt and dirt and other debris. Cleaning that can be darned near impossible except by...digging it out (sound familiar?), cleaning the stone and replacing it, or installing new stone. You can probably put the material back if it's at least washed down so it's just stone you're putting back, and not sand and clay, too.
But before you do any of that, at the bottom of your well (or excavation), dig a hole about 12" in diameter and maybe a little deeper. Then fill that hole with water and watch. When it drains, if it drains, fill it again. If the second fill disappears rapidly, try one more time. That will show you that the soil beneath what you're about to put back drains freely and quickly. If the water just sits, it doesn't matter what you put back in there, the water won't drain through the material below, and you'll have to install a drain. But first things first, try the simple stuff first.
As to the windows themselves, they may be old, yes. But they're not designed to be dams, and if the window well floods, water will come in, no matter what window you install. And remember that those windows are meant to open and ventilate, so closing them up solid wouldn't necessarily be a good solution.