If you're thinking of doing that yourself, it's risky even if you're competent at it....you can often read in the forums of owners who have replaced the screen correctly, but still have a non-working phone because the fault was not in fact with the screen....or if it was, there was also a fault elsewhere.
The advantage of putting your phone into the hands of repairers is that if the fault is simple, they'll find it and it won't cost too much, whereas if it's screen or something big, they'll replace it competently although in that case of course it would cost a lot.
It depends on how confident you are doing that sort of work yourself, but I suspect that it looks easier than it actually turns out to be.
A thought: have you perhaps got a duff SD card in the phone? A very long shot, admittedly.
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