Iphone 4 won't turn on and home button does not work

I went to a shop where there is a specialized department for iphone/ipad repairments (as suggested by @Tetsuiin). They told me the display was no longer working and it had to be replaced. They also replaced the home button. Now i got my iphone 4 back working like a charm again.

By the way, i have noticed that my battery lasts more time. Looks like this new display uses less energy ;)

One thing I would recommend you doing is connect your iPhone to a computer and download Recboot from here. This tool allows you to go into recovery mode and get out of it should fix the problem. If not, restore from iTunes.