The Baby Desert Eagle is not a striker fired gun, but rather a DA/SA trigger dropping a hammer on a spring loaded firing pin.
Following your schematic in your owners manual, I would remove the slide, remove the firing pin stop and firing pin. It sounds like you may have some contamination in the firing pin bore, perhaps a broken firing pin spring. Based on your description of "it works, it works, it don't work so well... it don't work at all"... that would be the simple, basic issue.
The other would be that, although I'm not real familiar with the Baby Desert Eagle other than it's a variation of the CZ75... if it has a firing pin block like the CZ75B, which through a lever and plunger arrangement blocks the firing pin from forward movement unless the trigger is pulled... some element of that may be faulty and restricting the firing pin. You can, to a limited degree, see this lever in operation if you remove the slide and cycle the trigger. Don't let the hammer fall on the frame.
As you say it's a new gun, if you can't quickly and easily correct the problem within your abilities, send it back to Magnum Research.
C
