If your iPhone 4 switch quickly between "Searching" and "No service" after a fall or an attempt to repair the screen, you may have damaged the blue coil inductor, present near the battery connector (see picture)
This component is here to pre-amplify (moderately) the GSM signal between the antenna and the oscillator who filter out unwanted frequencies.
This is not a totally vital component, and it may not be worth trying to change it.
You can find this component on eBay for 8 euros, but it will be difficult to weld without special CMS equipment an solid skills. Some folks can do it for sixty euros, but that is a little bit too much.
The best thing to do in my opinion, having tested it on two iPhone 4, is to make a jumper with tin or a copper wire between the two legs of the lost component, and you will get your signal back.
I then made in a few seconds a mere trace of tin soldering between the two legs of the inductor, and I got five bars of network on an iPhone 4 that was picking absolutely nothing.
Of course, even if it is at the reach of anybody, it is still better to perform the operation under a magnifying glass, without trembling, and especially not to insist on temperature. There are vital components such as baseband nearby, and the surface is very small, so there is no need for too much heat.
Some guys are using heat gun. I would not recommend it for the same reason (too much heat, small surface, vital components nearby).
I saw on some sites that you could also make a jumper in case of loss of the oscillator (the golden circle component to the left of the blue inductor in the image).
I would not recommend it. Frequencies will not be filtered at all, and there will be virtually no protection between the antenna and the input signal in the baseband.