If you are contracting in a situation like this a reasonable rate could mean $250-$1000 an hour. Really depends on what kind of money your currently make.
A better approach in the case would be to offer to investigate, and provide a flat rate. You can charge $3000 flat fee, and you may solve it in 1.5 hrs.
Oh god yes. Otherwise it's always the same: try to bargain you down to billing 30 minutes work, then complaining that you didn't do the 1.5h of work they'd agreed wouldn't be done to save costs. The usual "in lieu of paying you more, we'll complain harder" nonsense every client from hell pulls.
Or just set a day rate, and limit scope to helping with the specific problem. "It's $1200/day, and scope is limited to helping you understand how to recover from the described problem. All of the work recovery work will be done by you, and my role will be limited to advising."
