Is my PC wifi compatible?

Network Adapter: Realtek PCIe FE Family Controller

That's the Ethernet not the wireless. Check the device manager for hardware IDs:

http://dellwindowsreinstallationguide.com/downloading-drivers-checking-hardware-ids-and-downloading-and-installing-dell-system-drivers-in-the-correct-order/checking-hardware-ids-in-the-device-manager/

There are wireless card drivers (DW1505, DW1525) for this model but may have been optional at the time of purchase. You can however find one of the cards on eBay and install it or alternatively, the easiest is just to use a USB dongle.

http://www.amazon.co.uk/Belkin-Wireless-N300-USB-Adapter/dp/B0052CJU3O/ref=pd_cp_computers_0/277-6462516-5471841