Help Needed To Improve The Performance Of The Query

Hello,
I have the following setup and I would appreciate any help in improving
the performance of the query.

BigTable:
Column1 (indexed)
Column2 (indexed)
Column3 (no index)
Column4 (no index)


select
[time] =
CASE
when BT.Column3 = 'value1' then DateAdd(...)
when BT.Column3 in ('value2', 'value3') then DateAdd(...)
END,
Duration =
CASE
when BT.Column3 = 'value1' then DateDiff(...)
when BT.Column3 in ('value2', 'value3') then DateDiff(ss,
BT.OrigTime, (select TOP 1 X.OrigTime from BigTable X where X.Column1 >
BT.Column1 and X.Column3 <> 'value4' order by X.Column1 ))
END,

FROM
BigTable BT where BT.Column3 = 'value1' OR (BT.Column3 in ('value2',
'value3') and BT.Column4 <> (select X.Column4 from BigTable X where
X.Column1 = BT.Column1 and X.Column3 = 'Value1'))


Apart from the above mentioned, there are a few more columns which are
just a part of select statement and are not in any condition statments.

The BigTable has around 1 Mil records and the response time is very
poor, it takes around 3 mins to retrieve the records (which would be
around 500K)

With the Statistics ON,
I get the following:

Table 'BigTable'. Scan count 2, logical reads 44184, physical reads 0,
read-ahead reads 0.
Table 'WorkTable'. Scan count 541221, logical reads 4873218, physical
reads 0, read-ahead reads 0.

Is there any way to increase the performance, so that I can get the
result under 1 minute?
Any help would be appreciated.

P.S: I tried indexing the Column3, but no improvement.