OK, did as you said. Then, to make sure I was hopefully giving you useful data, I re-opened the Time Machines preference, and attempted to click the button again. Copied below is the log data that was generated:
11/19/13 5:04:51.164 PM com.apple.backupd-helper[83]: Not starting scheduled Time Machine backup: No destinations resolvable
11/19/13 5:04:52.311 PM System Events[527]: .sdef warning for part of complex type 'number | boolean | date | list | record | text | any | data' used in suite 'Property List Suite': 'data' is not a valid type name.
11/19/13 5:04:52.312 PM System Events[527]: .sdef warning for type 'text | missing value | any' attribute 'uniqueID' of class 'XML element' in suite 'XML Suite': AppleScript ID references may not work for this property because its type is not NSNumber- or NSString-derived.
11/19/13 5:05:42.550 PM System Preferences[506]: *** Assertion failure in -[NSSecureColor initWithColor:], /SourceCache/ViewBridge/ViewBridge-46/NSSecureColor.m:32
11/19/13 5:05:42.552 PM System Preferences[506]: -[NSRemoteView viewDidMoveToWindow] caught non-fatal NSInternalInconsistencyException 'unable to convert NSNamedColorSpace System controlColor to Device RGB colorspace' with backtrace (
0 CoreFoundation 0x00007fff8bf7d41c __exceptionPreprocess + 172
1 libobjc.A.dylib 0x00007fff94481e75 objc_exception_throw + 43
2 CoreFoundation 0x00007fff8bf7d1f8 +[NSException raise:format:arguments:] + 104
3 Foundation 0x00007fff8e2c8c61 -[NSAssertionHandler handleFailureInMethod:object:file:lineNumber:description:] + 189
4 ViewBridge 0x00007fff8b20a65c -[NSSecureColor initWithColor:] + 724
5 ViewBridge 0x00007fff8b20a36f +[NSSecureColor secureColorWithColor:] + 48
6 ViewBridge 0x00007fff8b22dcfb -[NSRemoteView sendFontSmoothingBackgroundColorToService:] + 40
7 ViewBridge 0x00007fff8b22ebf5 -[NSRemoteView viewDidMoveToWindow] + 197
8 AppKit 0x00007fff903f51d0 -[NSView _setWindow:] + 2899
9 AppKit 0x00007fff903f2804 -[NSView addSubview:] + 364
10 AppKit 0x00007fff90406953 -[NSFrameView addSubview:] + 45
11 AppKit 0x00007fff90414cb5 -[NSWindow setContentView:] + 511
12 ViewBridge 0x00007fff8b234868 rendezvousPanel + 895
13 ViewBridge 0x00007fff8b233f3f -[NSRemoteView beginSheet:modalForWindow:size:isCritical:styleMask:] + 420
14 ViewBridge 0x00007fff8b234eea -[NSRemoteView beginDeferredSheet:] + 209
15 ViewBridge 0x00007fff8b235098 -[NSRemoteView beginDeferredSheets] + 283
16 ViewBridge 0x00007fff8b239ca2 __85-[NSRemoteViewMarshal beginSheet:modalForWindow:size:isCritical:styleMask:withReply:]_block_invoke + 83
17 ViewBridge 0x00007fff8b23d892 __deferBlockOntoMainThread_block_invoke_3 + 441
18 CoreFoundation 0x00007fff8beae7cc __CFRUNLOOP_IS_CALLING_OUT_TO_A_BLOCK__ + 12
19 CoreFoundation 0x00007fff8be9fee5 __CFRunLoopDoBlocks + 341
20 CoreFoundation 0x00007fff8be9fc6e __CFRunLoopRun + 1982
21 CoreFoundation 0x00007fff8be9f275 CFRunLoopRunSpecific + 309
22 HIToolbox 0x00007fff8f8e9f0d RunCurrentEventLoopInMode + 226
23 HIToolbox 0x00007fff8f8e9cb7 ReceiveNextEventCommon + 479
24 HIToolbox 0x00007fff8f8e9abc _BlockUntilNextEventMatchingListInModeWithFilter + 65
25 AppKit 0x00007fff903de28e _DPSNextEvent + 1434
26 AppKit 0x00007fff903dd8db -[NSApplication nextEventMatchingMask:untilDate:inMode:dequeue:] + 122
27 AppKit 0x00007fff903d19cc -[NSApplication run] + 553
28 AppKit 0x00007fff903bc803 NSApplicationMain + 940
29 libdyld.dylib 0x00007fff93adf5fd start + 1
)
timestamp: 17:05:42.552 Tuesday 19 November 2013
process/thread/queue: System Preferences (506) / 0x7fff77bb7310 / com.apple.main-thread
code: line 607 of /SourceCache/ViewBridge/ViewBridge-46/ViewBridgeUtilities.m in logCaughtException
domain: exceptions
11/19/13 5:05:42.553 PM System Preferences[506]: -[NSRemoteView beginDeferredSheets] caught non-fatal NSInternalInconsistencyException 'unable to convert NSNamedColorSpace System controlColor to Device RGB colorspace' with backtrace (
0 CoreFoundation 0x00007fff8bf7d41c __exceptionPreprocess + 172
1 libobjc.A.dylib 0x00007fff94481e75 objc_exception_throw + 43
2 CoreFoundation 0x00007fff8bf7d1f8 +[NSException raise:format:arguments:] + 104
3 Foundation 0x00007fff8e2c8c61 -[NSAssertionHandler handleFailureInMethod:object:file:lineNumber:description:] + 189
4 ViewBridge 0x00007fff8b20a65c -[NSSecureColor initWithColor:] + 724
5 ViewBridge 0x00007fff8b20a36f +[NSSecureColor secureColorWithColor:] + 48
6 ViewBridge 0x00007fff8b22dcfb -[NSRemoteView sendFontSmoothingBackgroundColorToService:] + 40
7 ViewBridge 0x00007fff8b22ebf5 -[NSRemoteView viewDidMoveToWindow] + 197
8 AppKit 0x00007fff903f51d0 -[NSView _setWindow:] + 2899
9 AppKit 0x00007fff903f2804 -[NSView addSubview:] + 364
10 AppKit 0x00007fff90406953 -[NSFrameView addSubview:] + 45
11 AppKit 0x00007fff90414cb5 -[NSWindow setContentView:] + 511
12 ViewBridge 0x00007fff8b234868 rendezvousPanel + 895
13 ViewBridge 0x00007fff8b233f3f -[NSRemoteView beginSheet:modalForWindow:size:isCritical:styleMask:] + 420
14 ViewBridge 0x00007fff8b234eea -[NSRemoteView beginDeferredSheet:] + 209
15 ViewBridge 0x00007fff8b235098 -[NSRemoteView beginDeferredSheets] + 283
16 ViewBridge 0x00007fff8b239ca2 __85-[NSRemoteViewMarshal beginSheet:modalForWindow:size:isCritical:styleMask:withReply:]_block_invoke + 83
17 ViewBridge 0x00007fff8b23d892 __deferBlockOntoMainThread_block_invoke_3 + 441
18 CoreFoundation 0x00007fff8beae7cc __CFRUNLOOP_IS_CALLING_OUT_TO_A_BLOCK__ + 12
19 CoreFoundation 0x00007fff8be9fee5 __CFRunLoopDoBlocks + 341
20 CoreFoundation 0x00007fff8be9fc6e __CFRunLoopRun + 1982
21 CoreFoundation 0x00007fff8be9f275 CFRunLoopRunSpecific + 309
22 HIToolbox 0x00007fff8f8e9f0d RunCurrentEventLoopInMode + 226
23 HIToolbox 0x00007fff8f8e9cb7 ReceiveNextEventCommon + 479
24 HIToolbox 0x00007fff8f8e9abc _BlockUntilNextEventMatchingListInModeWithFilter + 65
25 AppKit 0x00007fff903de28e _DPSNextEvent + 1434
26 AppKit 0x00007fff903dd8db -[NSApplication nextEventMatchingMask:untilDate:inMode:dequeue:] + 122
27 AppKit 0x00007fff903d19cc -[NSApplication run] + 553
28 AppKit 0x00007fff903bc803 NSApplicationMain + 940
29 libdyld.dylib 0x00007fff93adf5fd start + 1
)
timestamp: 17:05:42.553 Tuesday 19 November 2013
process/thread/queue: System Preferences (506) / 0x7fff77bb7310 / com.apple.main-thread
code: line 607 of /SourceCache/ViewBridge/ViewBridge-46/ViewBridgeUtilities.m in logCaughtException
domain: exceptions