[Glirdan]

He probably did not take the Ring because he knew what fate befell his brother and maybe he thought that the same thing could have happened to him if he succumbed to the will of the Ring.

As for the part about not letting Frodo carry the Ring to Minas Tirith, I believe he thought that since Frodo carried it all the way from the Shire, he wouldn't loose it. And even if Frodo did loose the Ring, they would probably end up finding it again because he had the Ring in his possession for a long time and the lure of the Ring would be to great for him to endure, just like Gollum.