We gave it our best shot, but we still don't know what's wrong with the computer.
give (something) (one's) best shot
To put one's utmost energy, effort, or determination into doing something. I gave writing my best shot, but I just don't think I can make a career out of it.Don't worry about being new, just give it your best shot.
give something one's best shot
and give one's best
Fig. to give a task one's best effort. I gave the project my best shot.Sure, try it. Give it your best!