Suddenly, events entered in Calendar on iPhone are not showing up in iCal or iCloud

Question

Until late November, i had an iPhone 4s with iOS 5.   Then i got an iPhone 6 with iOS 8.  As previously, when i would enter an event in the Calendar, that data would also show up in my iCal calendar and on my iCloud calendar, until the last couple of days.  Now, new entries are not showing up on iCal or iCloud.  I encountered the problem that my iPhone, 64G, is being backed up to the iCloud and after two backups, taking up 2.4G each, my 5G of iCloud storage was used up.  I speculated that this was why my phone data stopped syncing to the other calendars on the computer and cloud, though i did not know for sure.  I deleted one of the two back ups and am about to delete the other one.  I have never had this problem of running out of iCloud storage on my other phone.  According to Settings>iCloud>Storage, i had 89MB.  But since i have deleted one of the 2.4G backups (which was "incomplete") my new entries are still not showing up in iCal and on the iCloud.
Is there a way to get this feature to work again?
Are there things i can check or uncheck in settings or in Calendar or  ??   that will get this to work well as it did in iOS 5?

Answer 1

ckuan -  thank you for replying.  i am really desperate for help.  I have wasted so much time on this. I was on hold with Apple support for a long time and then had a call with a rep that lasted over an hour but he didn't know anything about issues of these kinds.  i was put on hold a lot while he consulted.  He did agree that the data wasn't syncing from iPhone to iCloud and iCal because the iCloud storage was used up by the iPhone back ups.  So he advised deleting one of them.  I now have 2.4G of storage on iCloud.  Am i wrong to think that should be enough?   I still ave the original complete back up (2.4g) undeleted, in case there some reason that i need it. i don't like deleting things i don't have a good understanding of.
Following your instructions, i went to Settings>Mail,Contacts,Calendars.  I then scrolled down to Calendars and at the bottom, i see where it says Default Calendar.  This raised new questions for me which i will ask you/others now:
On the Default Calendar page, there is a heading that says iCloud and there is a second heading that says my gmail email address, [email protected].  Under the iCloud heading, there is a list of 8 "calendars," called Work, Family, Pets, Home, etc.  Under the gmail address heading, there is only one option listed, which is my gmail username.  When i went to the Default Calendar option, as i think you suggested if i understood you right, i found that the Calendar with the checkmark next to it was the gmail user name, under the gmail address heading.  Presumably, this is the same setting i had on my 4s with iOS 5.
I wanted to follow your instruction to change this to iCloud as Default Calendar. but the only option i have is to choose only one of those 8 "calendars," either Work, or Pets, or Home, etc.  Does this make sense?   The only reason i know for having these many different calendars was to give different colors to the different event categories. I didn't really want them to be separate calendars. i just wanted to use the color coding for type of event in my overall calendar.
I don't know why this is suddenly so complicated and confusing, after working fine  for the first two or three weeks i've had the new iPhone.  Suddenly, when i enter events in Calendar, it's not reaching the cloud.  If this is because my gmail and/or google user name was checked as the default calendar, that was not a setting i would've recently changed.  I never would  have set my iPhone to only use one of the iCloud sub-calendars at my default calendars.
But right now, per your instructions, i have checked Settings>Mail.Contacts,Calendars>Calendars>Default Calendar to iCloud>Home (Home being one of my 8 sub-calendars).  When i look on the Mail,Contacts,Calendars setting list, under Default calendar, it now says Home, instead of my gmail username.  Just to be clear, there is no way to check iCloud on the Default Calendar page.  i have tried checking it, but it's just a somewhat grayed out heading and doesn't respond to attempts to check it, it's not offered as a Calendar option. Only the various sub-calendars are offered a default calendar options, under the grayed out iCloud heading.  So, i selected Home, for no particular reason. i have lots of entries under different categories.
Here is the result:   still no new entries showed up in iCloud or iCal.  In January, a couple of days ago,  i entered three dental appointments, for which i have always used Health as what i thought was a category (not a separate  "calendar").  The color of Health events is green.  The color of Home events is Blue.  After changing the Default Calendar from gmail email address>user name to iCloud>Home (blue), the dental appointment in January did not show up.  But when i went into the first dental appointment event>edit and changed the "calendar" to Home, it then showed up on the calendar.  The other two dental appointments which were still Health did not show up. 
Then, i changed the first dental appointment that is showing up in January back to Health (green).  It still shows up, now, colored green, even though Home/blue is now my default calendar.  But the two other dental appointments are not showing up.
Does this mean if want to use my Calendar and have the data backed up in iCloud and iCal, from now on, i need to use only one sub calendar and give up  using the different color codes because iOS 8 is forcing me to choose only one sub calendar to be my whole calendar, and the only way to use different colors for different categories of events would be to first enter it as the default sub calendar (such as dental appointment>Home), and then go back and edit it into the correct sub calendar (such as changing it to the correct category, Health) to show the correct one instead of the "default" one?
Why was this made so much more difficult and complicated than it used to be?  It was working normally up  until a couple of days ago.
What i need, if possible, is info on what setting i can use to go back to using my gmail address user name as my default calendar, so that it can just work properly as it did before.  It seems ridiculous that i am forced by iCloud to use a sub category as my default calendar and everything that isn't entered as that subcategory will not be processed in iCloud.  Why does iCloud provide these sub calendar category options at all, if it's going to force people to only be able to use one of them?
What am i missing here?
Is there a setting that would enable combining all subcategories as one calendar, called iCloud, but where i could still use the different colors for different categories?