If we don't go to heaven or hell, then what motivates us to serve God?

Our love for God motivates us to serve Him.

Must there be a reward or a threat for simply doing the right thing?

For example, do we wish to please our parents simply because we may get something out of it?

We owe Jehovah God everything. But not just that, also "God loved the world so much that he gave his only-begotten Son." (John 3:16) We cannot possibly pay Him back for all that He has done for us. The least that we can do is to try and follow His requirements for us:

"The conclusion of the matter, everything having been heard, is: Fear the [true] God and keep his commandments. For this is the whole [obligation] of man." (Eccl. 12:13)

And even keeping God's commandments aren't burdensome but are for our own benefit! "For this is what the love of God means, that we observe his commandments; and yet his commandments are not burdensome." (1 John 5:3)

We should consider ourselves fortunate and eternally grateful just to have the average longevity of 70 to 80 years of precious life that we do enjoy. (Ps. 90:10) But Jehovah God loves us so much that He has even provided for us a future promise of restoring a physical paradise on Earth and living forever upon it.

The more we learn about Jehovah, the more our love for Him grows and motivates us to serve Him.

For more, see

You Can Believe in a Paradise Earth