Is the God we pray to the same God Daniel prayed to?
Yes. The context states that the God Daniel prayed to is the same God believers pray to today, though under a different economy. Daniel appealed to God's mercy and grace, not his own righteousness, and that same God is the one we approach today.
Les teaches that Daniel, under law, prayed for Israel and Jerusalem, calling on God's mercy and grace even without full knowledge of the grace of God. Les explains that although believers today are under a different economy, the God they pray to is the same God Daniel addressed. Les then transitions to Philippians 4 to show how prayer commands differ in the New Testament.