I have a firewire port on the front of my case but my motherboard doesn't have a connection for it. Is there a way to internally convert a USB connection on the motherboard to a firewire connection?
You can get an external USB to firewire adapter that connects to a USB port, you can also probably find a media expansion bay with a firewire port that uses the internal USB header.
Short answer: no. Firewire, while essentially the same structurally as USB, is faster than USB2, and it patterns the data differently. There are Firewire adapters as Razear mentioned, but you will be seeing a significant drop in data rate if you plug a camcorder (or other Firewire device) into it.
The simplest way is to pop in a PCI card that has an internal Firewire header, like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16815124034
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