MacBook – Mac does not sleep

There is a week or so since my macbook stopped being able to go sleep, instead it stops by just sleeping the screen, while the system light does not go blinking (and the system won't go sleep either, as it returns really fast when one key is stroke). Although this does not seems to influence, just for complementary information I have OS X 10.9.4. I've made some research on this issue, and the best topics I've found, for they contain almost every other topics answers in a clear and brief way, can be found here and here.

I've followed even before finding the linked topic all instructions, that is:

• I do not have any sharing options enabled (System Preferences →
  Sharing).
• I do not have "Wake for network access" enabled (System
  Preferences → Energy Saver).
• It does not matter if the Mac is connected to a power source.
• I've reset the SMC and the PRAM, but this did not help.

and also:

• I've restarted my mac on safe mode, and tried to enter on sleep mode, but also unsuccessful.

So, as can be seem in many places, the next step is to check the power management log, by doing pmset -g pslog. By doing so, I've discovered the cause for my issue, but I have not found any solution for this problem but to change the power management system, and the alternatives seems only to exist for hackintoshes (as I've found out here). Next, I post the pmset log:

Logging IORegisterForSystemPower sleep/wake messages
pmset is in logging mode now. Hit ctrl-c to exit.
29.07.14 23:15:36 GMT-3  IOPSNotificationCreateRunLoopSource
Now drawing from 'AC Power'
 -InternalBattery-0 99%; charged; 0:00 remaining

29.07.14 23:15:50 GMT-3  IORegisterForSystemPower: ...Sleeping...
29.07.14 23:15:57 GMT-3  com.apple.system.powersources.lowbattery

29.07.14 23:15:58 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...
  wakeType = HID Activity

29.07.14 23:18:16 GMT-3  IORegisterForSystemPower: ...Sleeping...

29.07.14 23:18:23 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...
  wakeType = HID Activity

29.07.14 23:18:49 GMT-3  IORegisterForSystemPower: ...Sleeping...
29.07.14 23:19:31 GMT-3  com.apple.system.powersources.lowbattery

29.07.14 23:19:36 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...
  Wake Reason = OHC1
  wakeType = HID Activity

29.07.14 23:19:49 GMT-3  IORegisterForSystemPower: ...Sleeping...
29.07.14 23:20:03 GMT-3  com.apple.system.powersources.lowbattery

29.07.14 23:20:03 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...
  Wake Reason = OHC1
  wakeType = HID Activity

29.07.14 23:20:15 GMT-3  IORegisterForSystemPower: ...Sleeping...

29.07.14 23:21:06 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...
  Wake Reason = OHC1
  wakeType = HID Activity

I've tried to enter on sleep mode, via ->Sleep, which triggers:

29.07.14 23:19:49 GMT-3  IORegisterForSystemPower: ...Sleeping...
29.07.14 23:20:03 GMT-3  com.apple.system.powersources.lowbattery

and using DeepSleep, which does not triggers com.apple.system.powersources.lowbattery, but also doesn't enter on hibernation or sleep mode:

29.07.14 23:20:15 GMT-3  IORegisterForSystemPower: ...Sleeping...
29.07.14 23:21:06 GMT-3  IORegisterForSystemPower: ...HasPoweredOn...   
    Wake Reason = OHC1   wakeType = HID Activity
    wakeType = HID Activity

Although the log says I've the battery 99% charged, which is what is display on battery icon on workspace, it says that it has 0 minutes power left on it, which is wrong. How can I workaround this issue? One more information, my macbook says this when I click on the battery icon:

Service Battery: The battery is not functioning normally; but this
does not necessarily mean that you notice a change in the use or the
charging capacity. Bring your computer in for service. You can use the
battery until the review without any negative effects on your computer
still.

but I've used it for years on this state and had never any problem with it. My battery health is around 70% (I've used it for 4 years with the same battery), and it still works on battery for around 4 hours working.