basilisk - Why didn't Ron and Harry ask Professor McGonagall for help instead of Lockhart to enter the Chamber of Secrets?

After Harry and Ron discovered Hermione's note (torn from a book) and they figured out where the Chamber might be and that Slytherin's monster is a basilisk, they went to the staffroom. My question is why didn't they ask for help from a professor like McGonagall or Flitwick and went to Lockhart, instead.

I don't think that "because he is the DADA teacher" is a good answer, even if Harry says that when Lockhart refuses to help, because they knew that Lockhart was dumb. Moreover, when they arrived in the staffroom, professors Sprout, McGonagall, Snape and Flitwick were mocking Lockhart.

I believe that prof. McGonagall for example would've been incredibly useful in the Chamber of Secrets.

Regarding the fact that they believed that Lockhart will try to enter the Room:

Snape: Just the man.[...] Your moment has come at last.

McGonagall: That's got him out from under our feet.

Lockhart: "I - well, I - " sputtered Lockhart. "I - I really never - you may have misunderstood - "

Lockhart gazed desperately around him, but nobody came to the rescue. He didn't look remotely handsome anymore. His lip was trembling, and in the absence of his usually toothy grin, he looked weak-chinned and feeble.

I think that they had enough clues to figure out that Lockhart couldn't help them.

Answer

When they figured out what was in the Chamber and where the entrance was, they were going to go tell McGonagal.

‘What’re we going to do?’ said Ron, whose eyes were flashing. ‘Shall we go straight to McGonagall?’
‘Let’s go to the staff room,’ said Harry, jumping up. ‘She’ll be there in ten minutes, it’s nearly break.’

There they learn Ginny has been taken and hear Lockheart agree to go deal with it.

‘We’ll leave it to you, then, Gilderoy,’ said Professor McGonagall. ‘Tonight will be an excellent time to do it. We’ll make sure everyone’s out of your way. You’ll be able to tackle the monster all by yourself. A free rein at last.’
Lockhart gazed desperately around him, but nobody came to the rescue. He didn’t look remotely handsome any more. His lip was trembling, and in the absence of his usually toothy grin he looked weak-chinned and weedy.
‘V-very well,’ he said. ‘I’ll –I’ll be in my office, getting –getting ready.’
And he left the room.

They're upset about Ginny and retire to the common room to mourn. They're not old enough to understand that Gilderoy never intended to enter the chamber, or that the other teachers surely knew that. So, when Ron has one of his famously bright ideas...

‘D’you know what?’ said Ron, ‘I think we should go and see Lockhart. Tell him what we know. He’s going to try and get into the Chamber. We can tell him where we think it is, and tell him it’s a Basilisk in there.’

It seems like the best option they have. Harry himself believed Ginny was dead and their intention was to give an adult information that would be useful, not find someone to accompany them. They only decided to go themselves when Lockheart showed his true colours by trying to wipe their memories, at which point he became an unwilling meat shield as much as someone they believed would be useful.

It is reasonable to assume that after defeating an adult in a duel, of sorts, Harry thought himself quite the capable hero and was feeling the effects of adrenaline. His actual decision process of "why don't we go" isn't described, which makes me think it was a snap decision with little rational thinking behind it.