Hi Frank,
  Hi Clemens,
  I have to admit that I have been running out of
ideas why the wiki cannot get a connection while "curl" can.
 One last try: has the gateway connecting the local network to the internet an application
firewall or the like ?
 Something that sniffs user-agents for http connections and only allows "known
ones" ? 
 Not to my knowledge, but see below
> The java client used by the XWiki installation wizard might be emulated with:
>
>    curl --user-agent "history" 
http://extensions.xwiki.org 
bad info given by me here, sorry; it should read:
   curl --user-agent "XWikiExtensionManager"   
http://extensions.xwiki.org
anyway, this seems not to be the problem ... because the other bogus user agent works as
well:
 $ curl --user-agent "history" 
http://extensions.xwiki.org
 <!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
 <html><head>
 <title>302 Found</title>
 </head><body>
 <h1>Found</h1>
 <p>The document has moved <a
href="http://extensions.xwiki.org/xwiki/bin/view/Main/WebHome">…
 </body></html>
 $
  if this works, too, I have to admit I have no
clue why it does not work.
 (Btw, there should be an error message in the log files. Is there anything like that?)
 In fact, there is a single error being printed to logs/catalina.out /after/ I click the
"continue" button in the first step of the Distribution Manager:
 [...]
 2016-01-28 13:36:53,762 [Active Installs Ping Thread] WARN a.i.c.ActiveInstallsPingThread
- Failed to send Active Installation ping to [
http://extensions.xwiki.org/activeinstalls].
Error = [ConnectException: Connection timed out]. Will retry in [86400] seconds...
 [...]
 I don't know what an "Active Installation ping" is, but in fact while I
seem to be able to access this webpage:
 $ curl 
http://extensions.xwiki.org/activeinstalls
 {
   "status" : 200,
   "name" : "Bobster",
   "version" : {
     "number" : "1.1.1",
     "build_hash" : "f1585f096d3f3985e73456debdc1a0745f512bbc",
     "build_timestamp" : "2014-04-16T14:27:12Z",
     "build_snapshot" : false,
     "lucene_version" : "4.7"
   },
   "tagline" : "You Know, for Search"
 }
 $
 I cannot `ping` it:
 $ ping 
extensions.xwiki.org
 PING 
www.xwiki.org (104.31.71.57) 56(84) bytes of data.
 ^C
 --- 
www.xwiki.org ping statistics ---
 76 packets transmitted, 0 received, 100% packet loss, time 75445ms
 $
 Does the Distribution Manager execute a real "ping" command even though the
webpages are accessible?  And if yes, how can I avoid this?  I doubt that our networking
dept. will adapt any gateway configuration to to make a single software installation
possible :-} 
No, there is no ping or such; well, it relies on the library: "HTTP Components":
https://hc.apache.org/ to do the job.
I have to admit that I do not know exactly if this library does or does not send a ping
first, but I do not think it does.
Even if it were so, it is not the case of the problem, as I cannot ping
extensions.xwiki.org either, and install works from here.
The "timeout" error message seems to indicate that the connection never gets an
error but is simply dropped somewhere.
I do not think 
extensions.xwiki.org drops the connection - as you can get there via curl
...
Any chance the application server uses some proxy settings, as described at the following
link, but they happen to be incorrect?
http://platform.xwiki.org/xwiki/bin/view/AdminGuide/Installation#HRunningXW…
That might explain the timeout despite the server being able to reach the installation
repositories normally (i.e. via curl).
I have to admit that if it is not the proxy-settings then I am getting somewhat desperate
about how to diagnose the problem.
I guess one could try to get stack traces from the server while it is starting up
and use the java option "-Djavax.net.debug=all" (dumps lots of stuff to the
standard output) to see if it tries to open connections to 
extensions.xwiki.org
but I guess all one can get from that is that the server opens connections and then it
waits till timeout ...
If you just want to get the server running with a proper UI anyway, I have written up a
little HowTo :
 
http://platform.xwiki.org/xwiki/bin/view/AdminGuide/FillLocalMavenRepository
To use it, one needs to install + configure maven, however ...
I am still using maven 3.0.4 from
http://archive.apache.org/dist/maven/maven-3/3.0.4/binaries/apache-maven-3.…
but to just donwload the UI-packages any version of 3.x should "just work".
Clemens