Hello Janos,
Waow! Nice job ! 
I thought one moment I had the solution : a conflict on port 6405 (you can add this possible case to your troubleshooting guide) but after setting a new port and restarting SIA+Tomcat, I still have a problem.
In fact, now, netstat -a shows me that nothing is listening on port 6405, the RESTfull service port that I see in CMC !
Metrics of WACS are:
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Common Server Metrics
Machine Name VM-BOBI41.cloud.xyz
Name Server VM-BOBI41.cloud.xyz:6400
Registered Name com.seagatesoftware.img.osca.pjs."VM-BOBI41"-VM_BOBI41.WebApplicationContainerServer
Operating System Windows Server 2008 R2 (6.1)
Local Time Monday, 18 January 2016 23:09:38 o'clock CET
Version 14.1.7.1853
Start Time Monday, 18 January 2016 22:51:21 o'clock CET
PID 11920
Host Name VM-BOBI41.cloud.xyz
Host IP Address 12.34.56.78
Request Port 6417
Busy Server Threads 1
Adaptive Processing Server Metrics
Available Processors 4
Maximum Memory (MB) 1,820.5
Free Memory (MB) 191.863
Total Memory (MB) 693.5
CPU Usage Percentage (last 5 Minutes) 0%
CPU Usage Percentage (last 15 Minutes) 1%
Percentage of stopped system during GC (last 5 Minutes) 0%
Percentage of stopped system during GC (last 15 Minutes) 0%
Number of page faults during GC (last 5 Minutes) 0
Number of page faults during GC (last 15 Minutes) 0
Number of Full GCs 0
JVM Lock Contention Count 0
JVM Debug Info STATE_NOT_ACTIVE
JVM Version Info SAP Java Server VM (6.1.066 24.55-b13 May 7 2014 18:40:24 - 61_REL - optU - windows amd64 - 6 - bas2:217766 (mixed mode) compressed oops)
JVM Deadlocked Threads Counter 0
JVM Trace Flags { }
Services Business Process BI Service, Mobile BI Web Application Service, Mobile Configuration Web Application Service, Query Builder Service, SDK Services Web et service QaaWS, Service Web de type RESTFul, Service conteneur d'applications Web, Service d'audit, Service de journal de suivi, Service de l'application Web BOE
Threads in Transport Layer 9
Transport Layer Thread Pool Size 9
Auditing Metrics
Current Number of Auditing Events in the Queue 0
Web Application Container Server Metrics
List of Running WACS Connectors HTTP
Logging Service Metrics
Logging Directory C:/Program Files (x86)/SAP BusinessObjects/SAP BusinessObjects Enterprise XI 4.0/logging/
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Is it enough to see (in bold) in "Services" section : RESTful web service ?
That shows RESTful web service is present (installed) and should start ?
Obviously, it is not since nothing is listening on 6405 port... but WHY ??? 
Are there other things to check ?
Logs of WACS are quite similar to my 2nd post.
TESTS of URL
-3-
a) http://VM-BOBI41:6405/biprws
On standalone BI 4.1 SP7 server => "Connection failed" (normal since nothing is listening on this port)
On client side : same thing
b) http://vm-bobi41:8080/dswsbobje/
server : Axis2 welcome page OK
client : Axis2 welcome page OK
c) http://vm-bobi41:8080/dswsbobje/services/Session
On both client & server:
<Exception>org.apache.axis2.AxisFault: The endpoint reference (EPR) for the Operation not found is /dswsbobje/services/Session and the WSA Action = null. If this EPR was previously reachable, please contact the server administrator. at org.apache.axis2.engine.DispatchPhase.checkPostConditions(DispatchPhase.java:102) at org.apache.axis2.engine.Phase.invoke(Phase.java:329) at org.apache.axis2.engine.AxisEngine.invoke(AxisEngine.java:262)
...
Any idea to understand why RESTfull service does not start ?
Regards,
Stephane.