It should be pretty straightforward:
In [10]: df
Out[10]:
     a  b  c
0  NaN  9  7
1  1.0  7  6
2  5.0  9  1
3  7.0  4  0
4  NaN  2  3
5  2.0  4  6
6  6.0  3  6
7  0.0  2  7
8  9.0  1  4
9  2.0  9  3
In [11]: df.loc[df['a'].isnull(), 'b']
Out[11]:
0    9
4    2
Name: b, dtype: int32
UPDATE:
In [166]: df
Out[166]:
     a    b  c
0  NaN  5.0  3
1  7.0  NaN  8
2  4.0  9.0  7
3  8.0  NaN  9
4  3.0  0.0  5
5  NaN  3.0  5
6  9.0  0.0  3
7  0.0  2.0  6
8  7.0  8.0  7
9  1.0  7.0  6
In [163]: df[['a','b']].isnull().any(axis=1)
Out[163]:
0     True
1     True
2    False
3     True
4    False
5     True
6    False
7    False
8    False
9    False
dtype: bool
In [164]: df.loc[df[['a','b']].isnull().any(axis=1)]
Out[164]:
     a    b  c
0  NaN  5.0  3
1  7.0  NaN  8
3  8.0  NaN  9
5  NaN  3.0  5
In [165]: df.loc[df[['a','b']].isnull().any(axis=1), 'c']
Out[165]:
0    3
1    8
3    9
5    5
Name: c, dtype: int32