Q: how can i back-up my iphone online because my phone is broke and wont cut on.but i have pictures on there that i want .

You can use an iCloud Backup of your iPhone, see this link:    iCloud: Backup and restore overview

and also:   About backups in iCloud and iTunes - Apple Support

But to download your photos from the iPhone you do not need a backup -  connect the iPhone to a computer by USB and try to download the photos, for example using Image Capture on a Mac.

What exactly is the state of your iPhone?  What do you mean by "won't cut on"?

If you mean the iPhone will not turn on at all then there's no way to recover any of the data on it.  Make an appointment at the nearest Genius Bar for a free diagnosis to see if Apple can help you.