Joe,

You said

Quote
This is exactly what I am saying. In THEIR OWN MINDS they thought they were doing God's will. They had this desire. The doctrine of total depravity is not against this thought.

What you say is simply not what the apostle Paul is saying in Romans 3:
Quote
9 What then? Are we better than they? Not at all; for we have already charged that both Jews and Greeks are all under sin;

10 as it is written,
"THERE IS NONE RIGHTEOUS, NOT EVEN ONE;
11 THERE IS NONE WHO UNDERSTANDS,
THERE IS NONE WHO SEEKS FOR GOD;
12 ALL HAVE TURNED ASIDE, TOGETHER THEY HAVE BECOME USELESS;
THERE IS NONE WHO DOES GOOD,
THERE IS NOT EVEN ONE."
13 "THEIR THROAT IS AN OPEN GRAVE,
WITH THEIR TONGUES THEY KEEP DECEIVING,"
"THE POISON OF ASPS IS UNDER THEIR LIPS";
14 "WHOSE MOUTH IS FULL OF CURSING AND BITTERNESS";
15 "THEIR FEET ARE SWIFT TO SHED BLOOD,
16 DESTRUCTION AND MISERY ARE IN THEIR PATHS,
17 AND THE PATH OF PEACE THEY HAVE NOT KNOWN."
18 "THERE IS NO FEAR OF GOD BEFORE THEIR EYES."

Paul's claim here is that There is NONE who seeks for God. He includes everyone. By our fallen nature, there is therefore not a single person that desires to serve God or who seeks his will. If God were to leave us to ourselves this world would have been an utterly terrible place. His common grace, however, prevents such a situation and we therefore see that unbelievers also has eg. some sense for rightousness. But that does not mean they have the desire to serve God.

Johan