When is the earliest time you can Daven Shacharis?
The following are the earliest times, not necessarily lechatechila;
Birchos Hashachar- even in the middle of the night, excepting hanosen lasechvi (machlokes) (if you will return to bed there are other modifications)
Korbanos- amud hashachar (if they mention the actual korbanos, otherwise you can say them before that)
P'sukei d'zimra- amud hashachar
krias shema- should not be said until misheyakir, but bediavad your yotzei from amud hashachar
Birchos Krias Shema- This is a machlokes and should preferably not be said before misheyakir
Tefila- amud hashachar
Bracha on talis- misheyakir
Bracha on tefilin- preferably misheyakir (ask your rav)
When amud hashachar and misheyakir are are debatable, ask your rav.
(If you need ref's for anything, let me know. These are spread out.)
Regarding Davening early it is best not to daven prior to Vasikin. However in times of great difficulty you may Daven as early as Misheyakir (Shulchan Oruch Orach Chaim 58:1). You may even start Davening before Misheyakir up to Yistabach and put on Talis and tefilin at Misheyakir.
The Shulchan Aruch: Orach Chaim: Siman 89 says that the ideal time to pray Sh'moneh Esrei is at Hanetz hachamah, when the sun shines on the top of the mountains (Mishnah B'rurah there). If one happens to daven after Amud HaShachar- when sun first breaks into the horizon- one fulfills his obligation.
The Mishnah B'rurah there infers from the language of the Shulchan Aruch that before the sun illuminates the East, even if Amud/Alos HaShachar occurs, one is not yotzeih even b'dieved. Although some disagree (See Biur Halachah), all seem to agree that before Alos itself, one is not yotzeih at all.