Clean the trigger assembly thoroughly with a non chlorinated brake cleaner to strip all the old gummed up lube out of the works. That is the reason that so many 700's have malfunctions and it is a known issue with them.
It it doesn't work then, check to see if the previous owner messed with any adjustments and has the overtravel set so tightly the sear just doesn't engage. That is another known issue with 700's - the adjustable triggers get Bubba gunsmited and are made worse, not better.
If after all that you perceive it's worn, damaged or beyond your ability, a new trigger might be in order. It also goes to if you can't figure it out, it's gunsmith level work in your regard, time to take it to a known good smith who does acknowledged good work with a reputation and a backlog of a few weeks. Fast is not your friend in finding smiths who can do reputable work.
At the present Remington is replacing any trigger sent in to them, the backlog is months, and it's court ordered. Some research on the net will bring out that the original design was less than robust about safety, but owner neglect and the use of the wrong lubricants and poor adjustments only add to the issues.
In my case mine's working fine and I don't plan to replacing the trigger. But, I haven't adjusted anything from the factory or used gummy lubricants on it. So, no harm no foul - and hundreds of thousands of owners like me have never had a problem. Those who have generally relate stories about how they adjusted the trigger and used water displacing sprays instead of gun oils. You be the judge.
