What caused the loss of "everything" on Swiftair Flight QY-2939?
Without an accident report to go on, we can't know what caused the situation they had.  In fact, from the two links that were posted, we don't REALLY know exactly what they had.  There is the description "we lost everything" from the radio, but that isn't consistent with the statement that they were able to fly headings.

So what follows is a comment on the possible, rather than a statement of what DID occur.

What I can piece together is that they seem to have lost their pitot-static system.  This would remove the airspeed and altitude from all displays, but would leave heading and attitude unaffected.  It would also allow them to fly an ILS approach, with distance from the runway and the on-glideslope indication giving them a way to approximate altitude on final.

There are comments about them climbing to VMC, which strongly implies that they had attitude instruments available.  Likewise, the comment about flying headings would suggest that they had INS information available, since the INS drives the heading indications in the 737-400.  Yes, they could fly headings off the wet compass, but that wouldn't give them attitude information, which they seem to have had.

I don't think the descriptions are consistent with losing the displays in the aircraft, because losing the EFIS displays in an EFIS 737-400 would mean they'd use the analog standby attitude indicator, but the analog airspeed &amp; altitude indications would likewise be available.

Based on all of this, my best guess is that the "we've lost everything" statement is more a reference to having lost all airspeed and altitude displays (along with some other data, including a fair bit of the FMC data that becomes invalid when the FMC doesn't have wind data to work with).  Was the statement a perfectly precise &amp; exact description of the loss of only (only!) the pitot/static instruments?  Not really, but in the stress of the moment it's entirely understandable that what gets said doesn't exactly match what you mean.

In a case like this, the lack of good airspeed information would be the biggest problem, although with reasonably light winds, GPS/INS groundspeed can be a reasonable proxy for your airspeed, and you're flying known pitch/power settings anyway.  Also working in their favor, they seem to have been pretty light, with only "3 souls on board" according to the radio.  So essentially an empty aircraft with something like 25,000 lbs of fuel.  That weight would work out to a fairly slow approach speed, but being light weight they could add 10 or 20 knots above what they think their IAS is (converting GS to IAS without having the winds at altitude is where the uncertainty comes in) and fly the faster speed.  With a heavy aircraft, being 20 knots over your target approach speed could make for issues getting the aircraft stopped on the runway, but with the lighter aircraft those issues are much easier to deal with.

From the one radio transmission caught on the video, they evidently did have radio altitudes from the EGPWS, which is a fair proxy for the altimeter -- albeit with limitations.  If the captain was flying the aircraft using the HUD, or if the EFIS displays on that aircraft include a flight-path vector display, then it's entirely possible to maintain level flight, even if what altitude that is can only be surmised.  (They might also have something in the cockpit that displayed GPS altitude for them -- depends on exactly what they had &amp; if they took the time to get to it.)

Also of note, both links state that the aircraft flew out 2 hours later, which would be consistent with a blockage of the pitot-static system that was cleared out fairly quickly, and at that point the jet is good to go.

Final comment: I'll reiterate, I'm NOT posting this as any sort of statement that "this is what must have happened there."  We don't have enough data to reach certain conclusions.  I'm only drawing inferences from what limited information we do have in those 2 links, and suggesting that the scenario I laid out seems to be consistent with what is in the article and the video, and thus seems to be the most likely explanation.  If new facts come to light, anything or everything above could be subject to revision.

From everything I can see, it was a nice job by the crew to bring the aircraft safely back on what had to be a pretty bad day at the office!