I'm looking for a firewire card that is compatible with the Dell inspiron 3847

Solution
Just about any PCIe (PCI express) firewire card should work.

Here are just a few:
StarTech 3-Port FireWire 800/400 (1394b/a) PCIe Card Adapter
SIIG 1394 3-port PCI Card Model NN-440012-S8
SIIG FireWire 1394a 2-Port PCIe Card, Model NN-E20012-S2
2-port of 1394b + 1-port of 1394a Firewire Ports PCI-Express Controller Card (SY-PEX30016)

If you are running Windows 8.0 or 8.1 you will need to download the legacy firewire driver from Microsoft.
Just about any PCIe (PCI express) firewire card should work.

Here are just a few:
StarTech 3-Port FireWire 800/400 (1394b/a) PCIe Card Adapter
SIIG 1394 3-port PCI Card Model NN-440012-S8
SIIG FireWire 1394a 2-Port PCIe Card, Model NN-E20012-S2
2-port of 1394b + 1-port of 1394a Firewire Ports PCI-Express Controller Card (SY-PEX30016)

If you are running Windows 8.0 or 8.1 you will need to download the legacy firewire driver from Microsoft.
 
Solution


What about the power supply connectors on these PCIe cards? Is there an adapter from the 4 pin power connector on the PCIe card to the Dell B300NM-01 PSU 15 pin SATA II connector?

Yes. Adapters can be purchased. I used a Citynet CC-S24P-A SATA II to Molex 4 pin

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