You first issue is with your friend's Dell power supply (PSU). It is likely that the PSU is not sufficient to power the HD4870 (requires 500W PSU). Also, for the HD4870 to work, it MUST be connected to the PCI-E external connectors. It will not work without the external power applied.
That being said, if your friend has the tower version of the 755, it should physically fit. Good luck!