Can I use a program run ability (eg: Sneakdoor Beta) and an run event card (eg: Account Siphon) for the same run?
No.

Each of these are a single 'click' to actually play.  Sneakdoor Beta specifically lists that you are using a click to use it's ability.  That click kicks off a run, but the click starts at using Sneakdoor Beta's card ability.  Once the run starts, you can no longer user clicks to play cards, use card abilities, ect.  On the same token, to play Account Siphon, you must use a click to play the event card.  As you do, the event card kicks off a run, but again, the click starts at playing a card ability.  This is all by design so you can't stack up a bunch of 'run' abilities.  It would also make other cards broken, like the event card for Shapers that lets you consider one piece of ice as all three types.

Things that will work?  Security Testing and Dirty Laundry.  +2 credits the first time you succesfully run a chosen server and +5 credits for completing a successful run on a server.  You use the click to play the event card and, since it was the first successful run on that server, you get the security testing instead of accessing cards.  Add in Desperado for a +1 credit after every successful run and play as Ken to get +1 credits from playing a run event and you're looking at a net of +7 credits for one run.  But that's just an example of the synergy that IS possible.