Mal.ka - go.dam - NE.MAR - u.pis.reh - hel.ma - de.nah ....
king the - before - WE WILL TELL - and the interpretation of it - dream the - This is...
Reading from right to left, in preferred English: This is the dream and the interpretation of it, WE WILL TELL, before the king.
NE.MAR...verb-Qal-imperfect...first person common plural.
The WE here, (in Dan 2:36), is in sharp contrast to the WE in Dan 2:4,7, where we see the Chaldeans - apart from the magicians, the conjurers and the sorcerers (see verse 2) - are before the king, imploring him to tell the dream to them, so that they (the WE) can declare the interpretation. In 2:36, the WE, it would seem, is referring to Daniel and his three fellow Hebrew friends, Hananiah, Mishael and Azariah, who subsequently were given the Babylonian names of, Shadrach, Meshach and Abednego.... Alternative thought processing has Daniel identifying himself with the likes of, all worshipers of Jehovah; divine wisdom; or even a contrasting force. God himself is even suggested (see Pulpit Commentary)....
In Dan, 2:17 & 18, we see Daniel informing his friends of the matter of interpreting Nebuchadnezzar's dream, Daniel having already been brought to the king's attention. We see that they all pray to God for compassion and understanding, in order that they may not be destroyed along with the rest of the so called wise men of Babylon.
Then, in Dan, 23, Daniel gives thanks and praise - after imparting wisdom and power to him - to God, for Him revealing the dream interpretation. The verse goes on to say..."Even now Thou hast made known to me what we requested of Thee, for Thou has made known to us the king's matter"...NASB.
In verses 46 thru 49, not only Daniel, but his three friends (thanks to a further request of the king from Daniel), also receive their rewards and thanks from the king, in no uncertain terms.
In Chapter 3, one can see the ultimate consummation of the WE, when Daniel lovingly relates the story of the same three friends when they are subjected to the fiery furnace, only to survive same through their own shared faith in God Almighty, who then go on to further prosper, in the province of Babylon.
In response to the last part of the question, as to why the ME went to the WE. Daniel having prayed, and presumably consulted, together with his three friends (Dan,2:18), unselfishly decided not to take all the credit, even though God singled him out solely for the dream interpretation (Dan,2:19) and even though he alone stood before the king "twice" (Dan, 2:16; Dan, 2:24-49). And, as if that was not enough of an unselfish disposition, Daniel also requested of Arioch, the king's commander, to spare the lives of the Babylonian astrologers, who had failed in their interpretation.