Grounds would be a good place to start. They need to be clean, and it does not hurt to upgrade them if you don't mind spending a couple of dollars. You can usually suspect grounding issues when 2 completely unrelated systems start having problems that affect one another. (window button changing the radio station was the craziest one i have seen to date) Clean the battery cables, the connections at the starter, back of the alternator, and fuse box. Be sure it is charging properly. Check the battery voltage when its running bad with a multimeter and be sure its identical to voltage when its running good. Low voltage can make a fuel injected engine act all kinds of stupid. Fuel pressure can be checked with a standard fuel pressure gauge at the schrader valve on the fuel line at the rear of the intake (slightly to the drivers side, should have a black cap screwed on it).