Not a lot of people know this, but I was once an agony uncle on an internet dating site. "K & Fi" of the now sadly defunct Snogg asked me to guest star. Here, for your delectation and enjoyment (or something) is my first effort...
"Dear Mr R - I send so many messages to all the women on your website but get very few responses. How can I increase the number of positive replies? My star sign is Virgo."
Ah, those fickle women - how rude of them to ignore you, eh? But walk a few yards in their shoes. Like it or not, it's a fact that us guys usually make the first move, and most women expect us to. I don't make the rules, that's just the way it is, even in 2003. So what happens? They get swamped with messages, quickly dashing their fine resolutions to politely reply to every single one.
My first piece of advice has been said again and again, but it bears repeating: don't cut and paste your message; send something that shows you've actually read and understood her profile. Comment on something she said; make it relevant, not generic.
Second: a little persistence goes a long way. If you don't hear back from her, feel free to try again! Perhaps you caught her at a bad time? Maybe she's been on holiday, and can't possibly wade through the hundreds of messages waiting for her on her return? I suggest trying again after a week, and once again after a couple more weeks. My personal rule is send three messages before giving up, but no more (don't be a stalker).
Last, but not least: not too long, not too short. Don't send War And Peace (it's scary) but make it a bit more interesting than "Hi, how are you?" As my old friend Madame "Smiler" Zelda always says, "Everyone likes a happy medium." ... Errrm, sorry...
Best of luck,