[SOLVED -- the problem was apparently due to the myIsam engine. No performance issue with innoDB]
[Also want to add that support is stellar]
The table has 60+M rows. Primary index is CHAR(11).
On my laptop, SELECT COUNT(*) from myTable WHERE myIndex > '-';
runs in about 30s (for 107M rows). On PA I killed the process after 20 minutes...
SHOW INDEX myTable doesn't suggest that the index is disabled. (no such comment) so I suppose that the problem is caused by an exceedingly small index buffer.
Can someone confirm the cause and suggest a fix?
[EDIT] Actually, all SELECT queries are extremely slow, more than an order of magnitude slower than on a puny laptop.
I ended up splitting the master table in much smaller ones (60M -> 2M) and things are back to acceptable.