MySQL multiple index - stuck with large query

[Sleeps]

I am stuck on a query I am trying to perform on a v large database (over 100 million tuples) and need to either optimize it somehow or create better indexes. The query is as follows (which gives the correct results on a small test database):

SELECT * FROM Results
WHERE Name = 'Chr1'
AND ( (Start >= 16300 AND Start <= 16400)
OR (End >= 16300 AND End <= 16400)
OR (Start < 16300 AND End > 16400) );

This query never completes so I am a bit stuck. I have created a multi index on the Name, Start and End columns using:

ALTER TABLE Results ADD INDEX (Name, Start, End);

If anyone has any ideas how to optimize the query or if I should be creating other indexes help would be much appreciated!

Also here is what an EXPLAIN gives for this query:
+----+-------------+-------------+------+---------------+-------+---------+-------+---------+-------------+
¦ id ¦ select_type ¦ table ¦ type ¦ possible_keys ¦ key ¦ key_len ¦ ref ¦ rows ¦ Extra ¦
+----+-------------+-------------+------+---------------+-------+---------+-------+---------+-------------+
¦ 1 ¦ SIMPLE ¦ Results ¦ ref ¦ Name ¦ Name ¦ 17 ¦ const ¦ 7757498 ¦ Using where ¦
+----+-------------+-------------+------+---------------+-------+---------+-------+---------+-------------+
1 row in set (0.02 sec)

[Demaestro]

What are the data types for the fields Start and End?

[SeanW]

Create separate indexes on start and end. With your composite index, mysql can not use the start and end fields to reduce the number of rows.

Sean