Hi,
It's possible to install Orthanc on a NAS Synology, I did it today (Orthanc 0.7.6 and Synology DS241+ DSM 5.0-4493 Update 2). But not directly with the OS of synology, through a chroot of a debian "Wheezy" installed on the NAS.
Prerequisities :
1) Add package repository
http://packages.synocommunity.com/2) Install Python 2.7.3.3 from SynoCommunity
3) Install Debian Chroot (wheezy) from SynoCommunity
4) Enable SSH access (and/or telnet, but not secure) in settings (DSM manager)
5) Copy the folder of the sources of Orthanc ("~/Orthanc") on your NAS (many solutions, with "File Station" for example or ftp...)
6) Open in the firewall of the NAS the ports 8042 and 4242 (if closed)
7) PuTTY (or other terminal) – SSH\telnet to Synology, login as root, the password is the same as admin (it's possible to use another login, you will find tutorials on internet)
8) Copy the folder Orthanc in a sub-folder of "debian" (example : "# cp -r ~/Orthanc /volume1/debian/opt")
9) # cd /volume1
10) # ln -s /volume1/@appstore/debian-chroot/var/chroottarget debian
11) # mount -o bind /proc /volume1/debian/proc
12) # chroot debian /bin/bash (now, the chroot is working)
13) # cd /opt (if you use the command "ls", you will see normally the folder "Orthanc")
14) # mkdir OrthancBuild
15) # cd OrthancBuild
16) # echo “deb
http://ftp.fr.debian.org/debian wheezy main” > etc/apt/sources.list
17) # echo “deb
http://ftp.fr.debian.org/debian/ wheezy-updates main" >> etc/apt/sources.list
18) # echo “deb
http://security.debian.org/ wheezy/updates main" >> etc/apt/sources.list
19) # apt-get update
20) # apt-get install build-essential unzip cmake mercurial uuid-dev libcurl4-openssl-dev liblua5.1-0-dev libgtest-dev libpng-dev libsqlite3-dev libssl-dev zlib1g-dev libdcmtk2-dev libboost-all-dev libwrap0-dev libjsoncpp-dev
21) # cmake -DALLOW_DOWNLOADS=ON -DUSE_SYSTEM_MONGOOSE=OFF -DUSE_GTEST_DEBIAN_SOURCE_PACKAGE=ON -DENABLE_JPEG=OFF -DENABLE_JPEG_LOSSLESS=OFF /opt/Orthanc
22) # ./Orthanc --config=Configuration.json
23) # nano Configuration.json (change "RemoteAccessAllowed" to "true").
24) # ./Orthanc
25) Open your browser : "http://[ip_Synology]:8042"
Enjoy :-)
To kill the process, open a new terminal on the synology (ssh or telnet) and "# killall Orthanc" (the chroot will be closed at the same time)