We almost gave you everything that could have gone wrong.
I would suggest uninstalling the game completely then install it again, or it could be a fault of the game file/s, so try to get a diff copy of setup.
I reinstalled the game,and installed ivmp as it says to install,it still loads up singleplayer
Upload the "client.log" and "launcher.log" next time please. Anyway by looking at your game folder I can only say: check your cracks.
-launcher.log:15/04/2018 20:58:39.975 Launching GTA IV
15/04/2018 20:58:39.991 Launching the launcherHelper
15/04/2018 20:58:39.991 Launcher is up
15/04/2018 20:58:39.991 Done
serverlist.log:15/04/2018 20:58:31.333 Connected to ROOT
15/04/2018 20:58:31.801 Re-adding rows
15/04/2018 20:58:31.801 Done
15/04/2018 20:58:34.125 Key code: 17
15/04/2018 20:58:34.125 Result:
15/04/2018 20:58:34.156 Key code: 65
15/04/2018 20:58:34.156 Result: a
15/04/2018 20:58:34.468 Key code: 84
15/04/2018 20:58:34.468 Result: T
15/04/2018 20:58:34.468 Key code: 16
15/04/2018 20:58:34.468 Result:
15/04/2018 20:58:34.936 Key code: 73
15/04/2018 20:58:34.936 Result: i
15/04/2018 20:58:34.999 Key code: 78
15/04/2018 20:58:34.999 Result: n
15/04/2018 20:58:35.311 Key code: 84
15/04/2018 20:58:35.311 Result: T
15/04/2018 20:58:35.373 Key code: 16
15/04/2018 20:58:35.373 Result:
15/04/2018 20:58:35.623 Key code: 73
15/04/2018 20:58:35.623 Result: i
15/04/2018 20:58:35.654 Key code: 78
15/04/2018 20:58:35.654 Result: n
15/04/2018 20:58:37.105 INTERNET
15/04/2018 20:58:37.105 Deleting servers
15/04/2018 20:58:37.105 Deleting info rows
15/04/2018 20:58:37.105 Deleted
15/04/2018 20:58:37.105 Deleted
15/04/2018 20:58:37.105 Starting connection
15/04/2018 20:58:37.307 Peer is active
15/04/2018 20:58:37.307 Done
15/04/2018 20:58:37.307 FEATURED done
15/04/2018 20:58:37.463 MasterList connection is good
15/04/2018 20:58:37.463 Requesting servers with option: 2
15/04/2018 20:58:37.713 Argonath RPG 2.1
15/04/2018 20:58:37.760 Received all servers
15/04/2018 20:58:38.571 New row selected
15/04/2018 20:58:38.571 Deleting server details
15/04/2018 20:58:38.571 Done
15/04/2018 20:58:39.819 Connecting to: Argonath RPG 2.1
15/04/2018 20:58:39.819 Version check msg redefined, was: M:CONNECT:Argonath RPG 2.1~145.239.183.131
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15/04/2018 20:59:23.078 Re-adding rows
15/04/2018 20:59:23.078 Done
15/04/2018 20:59:23.078 Draw starts on next frame
15/04/2018 20:59:24.701 EXIT: Window handle no longer exists
15/04/2018 20:59:24.701 Draw has stopped