So, I have always thought woken was a word...and I stand by my opinion. But the computer tells me that woke is proper. Here is the sentence: She couldn't remember what had woken her up in the first place. I think it sounds right...is it?
Woken is a proper past participle of wake, so had woken is correct. Your computer was probably confused by the presence of up, not recognizing it as part of the idiom to wake up.
what cog said... and 'woke' would only be correct without the 'had' in front of it... this is a good example of why no one should rely on the grammar check of any computer program... the only checker you should use is your brain... aided by good grammar books/sites, if you need help...