I am proud to say that I am still using my iPhone 4 that I purchased more than 4 years ago!
That being noted, it's aged over the years, and a common issue myself and others have had is that thte home button on iPhones becomes unresponsive, often due to dust getting in behind the button and limiting the contact. This forces many people to use the on-screen home button (which is another tip itself!), but which can be really annoying to use.
What solved the problem for me was to use a bit of rubbing alcohol and patience!
First, turn off your phone. Then, use a Q-Tip to dab rubbing alcohol along the edges of the home button, and repeatedly press the button (quickly).
You will likely have to keep reapplying the rubbing alcohol, and the repeated pressing should free up the dust in the button mechanism. I did this for a few minutes and the dust/dirt literally was coming out along the edges of the button - use another q-tip to clear this away as you go.
Keep reapeating this process until dust/grit stops coming out, and then wipe away any excess rubbing alcohol.
Power up your phone, and with any luck, the dust will be clear of the mechanism, and your home button will be working like new again!