I've been alphabet hunting for a while

Jelly, 28 23 22 bytes

1 byte thanks to Dennis.

26RØAṙ;U$;Œl$
;Zẇ@þ¢FS

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Takes an array of strings.

Cheddar, 148 bytes

(s,b=65@"90,c?)->(|>27).map(->s has(b=b.slice(1)+b[0])||s has b.lower||(1|>3).map(j->(c=s.lines.turn(j).vfuse)has b||c has b.lower?1:0).sum?1:0).sum

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Non-copmeting, 146 132 bytes

This is the exact same as above except map(...?1:0).sum has become any(...).

(s,b=65@"90,c?)->(|>27).any(->s has(b=b.slice(1)+b[0])||s has b.lower||(1|>3).any(j->(c=s.lines.turn(j).vfuse)has b||c has b.lower))

Rather slow but it works ¯\_(ツ)_/¯ . added any function after challenge release date.

The input does not need to be padded with whitespaces. But if an input doesn't work, pad it with whitespaces to make rectangle. The turn function is really finicky and I'm not sure when it works and when it doesn't

Explanation

Loops through all possible cycles of alphabet. On each iteration check if the current cycle of alphabet exists in the string, if not, check if any of the possible rotations of the string have the alphabet.

Ungolfed

(str, a = 65@"90)->
  (|>27).any(->
    str has (a = a.slice(1) + a[0]) ||
    str has a.lower                 ||
    (1|>3).any(j ->
      (c = str.lines.turn(j).vfuse) has a ||
      c has a.lower
    )
  )

05AB1E, 43 bytes

A‚Duìvy26FÀD}})U|Dø€J)˜vXDgs`rFysk>ˆ}}¯O__

Explanation in short

Get different variations of alphabet (caps, no-caps, reversed, normal) and store in X.

A‚Duìvy26FÀD}})U

Get each row and column of input as a list of strings.

                 |Dø€J)˜

Check each such string if it contains a variation of the alphabet.

                        vXDgs`rFysk>ˆ}}

Sum and double negate, giving 1 for true and 0 for false.

                                       ¯O__

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