How important is the hash power in solving a block?
Hash power is like a lottery ticket. The more you buy the greater the chance you have that one of your tickets will match the drawn numbers. 

But a person with one ticket can also win just the same. Each ticket has the same chance. 

Having a higher hashrate simply gives you more chances to win within a given block frame. 

In the end it boils down to luck. But the more attempts/lotto tickets/hashpower means your odds of finally matching/winning/solving increase.