Hmm - sounds like the part overheated and the solder joints melted (while the part cracked from overheat and stress); you soldered it back in place, but I doubt it will work long in the condition it is in. What I linked to was the datasheet for the SMD (surface mount device) version of the 1n5819 diode; you just need to look that up on Mouser or Digikey, and purchase one or more (I would actually buy a few - it won't matter shipping-wise, and you might want to replace that other one and have a few on-hand for future needs - they probably don't cost much):
Digi-Key - 1N5819HW-FDICT-ND (Manufacturer - 1N5819HW-7-F)
48 cents each, or 10 for three dollars and some change - get the ten...
As far as a substitute, you would have to look at the datasheet and see if you can use something similar from a place like Radio Shack or Frys Electronics - you may be able to find something similar. But why, I just gave you the link above; put in the quantity, click "add to order", and check out...
On your part, there is a line - this represents the cathode side of the diode (it is polarity dependent!); some parts have a dot or an indentation to represent this side; you won't know until you have the new part in-hand. On the PCB, the silkscreen should show something similar to indicate which side is the cathode and which is a anode; you need to install it properly in order for it to work. Now, I don't know if you re-installed the one that fell off properly, or if it is no longer acting like a diode - you may have got lucky (50/50 chance), or it is just acting as a piece of wire or solder bridge (because it overheated and failed). Note that you shouldn't try to just bridge the pads with a piece of wire or something; that diode is there for a purpose - if the designer had wanted to not use a diode, believe me, they would've (it would have saved them a lot of money over 10 thousand units, say) - so don't do it; replace it with the proper part.
Note - I am assuming this part is a diode; its the closest thing I could find that matches your pics, sizes, and number on the part...