P0300 is a random misfire, which corresponds with the shaking, random dieing and loss of power - essentially this means that one or more cylinder is unable to complete the combustion cycle. If you're lucky you may also have a P030x code, which corresponds to a misfire in a particular cylinder (x), this can narrow down the culprit.

You can check the spark plugs by removing them from the engine and placing the outer metal body of the plug on a metal part of the car body, then get a friend to crank the engine over. It's best to disconnect the fuel injectors when you do this to reduce the risk of singed eyebrows, also you only want to crank, not start the engine. You should get a strong spark on each plug. Given that you've already replaced the coil packs, a weak or absent spark would probably indicate a loose control wire to the coil pack, bad control unit, or a problem with one of the sensors responsible for timing. If you still have them, check the condition of the old plugs. Under normal service the plugs should be lightly and evenly dusted with white or white-brown deposits. Carbon (black) deposits on the plug indicate an over-rich fuel mixture or oil getting into the cylinder. Wet oil on the plug also indicates an oil-leak into the cylinder and could indicate worn valve guides. I would suggest looking for one plug that looks different to the rest to narrow down the misbehaving cylinder, but I suspect you don't have them in order any more.

The next thing I would look at is the fuel injectors. Depending on the engine, you may need to remove these from the engine and test them individually, there's a video on youtube about cleaning fuel injectors with (I think) carb-cleaner and a syringe which would also indicate worn or leaky injectors. If you can test them in the engine though, disconect all spark plugs and injectors except the injector you want to test, remove the injector from the manifold and place it in a glass jar (not plastic as petrol can dissolve many plastics). Get a friend to crank over the engine for a few seconds and observe that you get a strong pulse from the injector. Repeat with each injector. If one injector is noticeably weaker than the rest it should be replaced or at least a clean attempted. If all injectors seem a little weak or don't expunge any fuel you could have a problem with the fuel pump or blocked fuel lines. It goes without saying that petrol is volatile so take care not to create any sparks or naked flames (this includes smoking) around exposed fuel. Also take extreme care around fuel injectors as the fuel is under extreme pressure which can penetrate the skin, you don't want that shit in your blood stream.

If the spark plugs and fuel supply seem fine, you're next step is to do a compression test, this involves screwing a pressure guage into the spark plug hole and cranking the engine (again with injectors/plugs disconnected so that the engine doesn't start). Gauges are available from most parts stores, but as this is likely to be a one-off it may be cheaper to get a mechanic to do the compression test, and possibly also a leakdown test. One cylinder with lower compression (related to peak PSI) than the rest would likely indicate worn (leaky) valves or worn piston rings on that cylinder, however if all cylinders have low compression it's probably time for an engine overhaul (unlikely on a 2005 model unless it has been severely abused).

If none of the above reveals anything of note, you may have a worn valve cam - basically the inlet or outlet valve isn't openning fully and the combustion cycle isn't allowed to initiate or complete. A simple check is to remove the valve cover and check the profile of the cam lobes. Compare them against each other to see if any one in particular is mis-shapened or worn down. Check for broken valve springs, loose retainers or bent valves. if applicable, check the valve clearances against the manufacturers recommendations.

Hopefully that should be of some help :)