The prefix a- has not one source but several different sources. Webster lists six different prefixes of the kind a-.
prefix 1 - shortening of in/on/at
prefix 2 - as in arise. Webster's explanation of this a- is a bit vague and dubious. My idea: arise might be connected with Latin oriri meaning to rise/arise
prefix 3 - as athirst/akin/anew - Webster: from/of
prefix 4 - as achromatic - Webster: without/not - No mention of the Greek prefix.
prefix 5 - related with Latin ab- meaning coming/moving from a point.
prefix 6 - related with Latin ad- meaning moving to a point and similiar ideas.
Source: Webster's Comprehensive Dictionary of the English Language.
I'm not sure whether Webster has all sources. He doesn't show the relation between English await and German er-warten or English awake and German erwecken/erwachen. The German prefix er- also has several meanings; in erwecken/erwachen it expresses the beginning of an action. Er- in erwarten makes warten transitiv. There are a lot more of these connections.