Well, I'm having a similar or even the same problem. Weird thing is, it worked for me on another OS. I used Linux Mint 15 64-Bit Cinnamon before, but I switched to KDE (fresh install). I already have the 32-bit libs.. and I'm not exactly sure why it fails. Note: There's not even a Steam windows popping up. Just nothing (if I don't start it by terminal and see the log, of course)

Running Steam on linuxmint 15 64-bit
STEAM_RUNTIME is enabled automatically
Installing breakpad exception handler for appid(steam)/version(1373418487_client)
Installing breakpad exception handler for appid(steam)/version(1373418487_client)
unlinked 0 orphaned pipes
Installing breakpad exception handler for appid(steam)/version(1373418487_client)
[0712/205633:WARNING:proxy_service.cc(958)] PAC support disabled because there is no system implementation
/home/buildbot/buildslave_steam/steam_rel_client_ubuntu12_linux/build/src/steamUI/../common/steam/client_api.cpp (287) : Assertion Fail: ClientAPI_InitGlobalInstance: InternalAPI_Init_Internal failed.

Assert( Assertion Failed: ClientAPI_InitGlobalInstance: InternalAPI_Init_Internal failed.
):/home/buildbot/buildslave_steam/steam_rel_client_ubuntu12_linux/build/src/steamUI/../common/steam/client_api.cpp:287

Installing breakpad exception handler for appid(steam)/version(1373418487_client)
Uploading dump (out-of-process) [proxy '']
/tmp/dumps/assert_20130712205633_5.dmp
/home/buildbot/buildslave_steam/steam_rel_client_ubuntu12_linux/build/src/steamUI/SteamStartup.cpp (648) : Assertion Failed: ! "There w a problem with your Steam installation.\n" "Please reinstall steam.\n"
unlinked 2 orphaned pipes
CAsyncIOManager: 0 threads terminating. 0 reads, 0 writes, 0 deferrals.
CAsyncIOManager: 59 single object sleeps, 0 multi object sleeps
CAsyncIOManager: 0 single object alertable sleeps, 1 multi object alertable sleeps
[2013-07-12 20:56:32] Startup - updater built Apr 30 2013 10:04:24
[2013-07-12 20:56:32] Verifying installation...
[2013-07-12 20:56:32] BVerifyInstalledFiles: ubuntu12_32/steam is 5543712 bytes, expected 5642843
[2013-07-12 20:56:32] Verification complete
[2013-07-12 20:56:32] BRepairInstalledFiles: ignoring bootstrap file ubuntu12_32/steam
Shutting down. . .
[2013-07-12 20:56:34] Shutdown
Finished uploading minidump (out-of-process): success = yes
response: CrashID=bp-c3b4a017-96f9-442c-93fc-882a02130712

Looks to be a corruption of your steam install, would you try running steam --reset and see if that repairs it.

That worked thank you so much

Closing as resolved.