Please view the definitions of 'part' as a noun from the LDOCE:http://www.ldoceonline.com/dictionary/part_1
'Part of' and 'a part of' in the example sentences have the same meaning.
a) I am proud to be a part of a group that...
b) I am proud to be part of a group that...
Now, here is the difference described in the Collins COBUILD*:
’ is a singular count noun:
• A part of
something is one of the pieces, sections, or elements that it consists of. I like that part of Cape Town…Respect is a very important part of an relationship.Part
is a noncount noun:
• If something or someone is part of
a group or organization, they belong to it or are included in it. …voting on whether to remain part of the Union or become independent.
If there is any distinction at all in terms of meaning, it is that ‘a part of’ is close in meaning to ‘a piece of’ -- a discrete piece with distinct borders, whereas ‘part of’ might refer to a more diffuse piece. The meanings seem to have nothing to do with the importance or lack of importance of the part.
Now, as you can see, ‘a part of’ something and ‘part of ‘ something can often be used interchangeably, and can certainly be used interchangeably in Thatguy’s sentences.
*Collins COBUILD English Dictionary. Harper Collins 1995