Looks like your theme uses the TimThumb image script to generate thumbnails. You can see from the path, that the src value showing where the image is located for TimThumb to process is empty:
<img src="http://erdemligenclik.net/wp-content/themes/wpmedyahaber/resim/timthumb.php?src=&w=215&h=124&zc=1" width="215" height="124" alt="Zafer Bangash’tan Ramazan Mesajı">
Now, TimThumb is an very old script that has had a recent security issue. It's possible your host is shutting down the script due to those concerns, so I would start by asking them to review their logs.