The word 'to' can be used as a preposition, an adverb or a particle that together with a verb forms a 'to-infintive'.
When it is a preposition, it should be followed by a noun, a noun phrase, a noun clause or a gerund.
The word 'to' in 'The key to' is a preposition. We use the word 'to' to bring out the goal that we want to achieve. Since it is a goal, it should be a noun.
Sometimes when we dont know whether the word 'to' in a sentence is a preposition or a particle, we can look at how the phrase is used in other sentences. As answer '001' has rightly pointed out, 'the key to sucess' is a good example. From the phrase 'the key to sucess', we know that the 'to' there is a preposition because the word 'sucess' is a noun.
'Allowing' is the gerund form of the verb 'allow'. Gerunds only function as nouns while participles only function as adlectives/adverbs. An Infinitive can be used as a noun, an adjective or an adverb.
I have uploaded a video 'Gerund and Participle" on Youtube. I hope you will find it useful.
https://www.youtube.com/watch?v=QuJCaiySNU0
2014-06-12 18:33:36 補充:
I agree with Godfrey. We should avoid making grammatical mistakes in our answers. In some of the answers in Yahoo Knowledge, there are many grammatical mistakes. Some students may not realize that and learn from them. As a result, they will follow suit and make the same mistakes themselves.
2014-06-12 18:43:51 補充:
Having said that, I must admit that 石破天驚 is one of the responsible ones. He has made a few mistakes. So do we! Let us joint hands to make this forum a success.