'As having won...' :(

Yes, although I would use "capture" instead of "take" and fix the comma splice.

I frequently check the most popular best sellers on your website, currently 'My Story' by John Smith takes my interest as having won the 2014 literacy prize.

What kind of tenses are these? I have never seen anything like it before.

When you speak the sentence aloud, I pause after website, so that is why I put a comma there. Explain?

AnonymousWhen you speak the sentence aloud, I pause after website, so that is why I put a comma there. Explain?

It is not one sentence. It is two sentences. When you put a comma (not a full stop or a semicolon) between two sentences, that is a grammatical error called a "comma splice."

I frequently check the most popular best sellers on your we

AnonymousWhat kind of tenses are these? I have never seen anything like it before.

The verbs in your sentences are both simple present tense.

I frequently check (simple present tense) the most popular best sellers on your website. Currently 'My Story' by John Smith takes (simple present tense) my interest as having

Very helpful, thanks. However, having looked at this website, sentences written with perfect participles break another rule: dangling participles. For example, 'having nowhere to sit, she stood at the back of the bus'.

It is forbidden to begin sentences with 'having', or so I was told. Is this true?

Anonymous Is this true?

No.

The following sentence is perfectly OK. The subject in participial clause is the same as the subject in the main clause.
'Having nowhere to sit, she stood at the back of the bus'.

The next sentence has a dangling participle and is incorrect:
Barking and growling loudly, Mary held tightly onto her dog's

Yes I can.

The sentence implies that Mary was barking and growling loudly, rather than her dog. So, the participle should go with the noun closest to it, either directly preceding or following it.

AnonymousYes I can.

By Jove, I think you've got it! A+++

AlpheccaStarsThe phrase "having won" is not an inflected verb. It is a form called the perfect participle. In traditional grammar, having won the 2014 literacy prize is called a gerund phrase.

As it's a (perfect) participle, it's a participle phrase.