Is this a Regal LS or GS? The fuel pressure can be checked at the fuel pressure regulator (FPR) Schrader valve. With vaccum connected it will read in a range of 45 - 55 psi. With vaccum dis-connected it should read around at least 52 psi. This will test the fuel pump, fuel filter and the FPR. There is also a fuel pump relay involved.
If you have a GS model it's a two speed pump and the fuel pump resistor may be bad. The GS has an additional relay - fuel pump speed control relay which works in conjunction with the resistor.
If fuel is good then it's possibly ignition. Based on your symptoms it could be a crankshaft position sensor or an ignition switch and harness assembly too.
