If it has a transponder immobiliser system then it sounds like the problem could be a high resistance in the reader coil (around the ignition barrel). From memory though I think the immobiliser is linked to the remote central locking.
Volvos are notriosly difficult to bypass the immobiliser on so it is generally easier to repair the fault.
I will upload a simple circuit you can build in a few minutes for a few quid (a max232, a few smoothing caps, a couple of resistors, a diode or two and a couple of bc547 transistors) that will read the fault codes from the immobiliser and angine ECU's when used with some software I have.
In the mean time however it might be wirth scoping your crankshaft and camshaft sensors (whilt cranking when it is not running). You are looking for a good strong sine wave with a regular break due to the missing tooth on the reluctor ring.