Mail Can't Open & com.apple.internetaccount process hogging 100% CPU

Question

Desperately seeking answers after Mavericks install..
My mail crashed and now won't open at all. I've tried most (if not all) the suggestions posted by others.  Haven't tried deleting and reinstalling mail yet, as this will be my last resort since I have a work account in it that is not on IMAP.
And another troubling issue is my macbook's fan is going crazy and feels like its overheating.
Looking at "Activity Monitor" I see a process "com.apple.internetaccounts" that is taking 100% CPU and 1.6GB of memory!!
No idea what this process is and can't seem to quit it.
PLEASE HELP!!! Thanks in advance
Using EtreCheck, pls see below report:
Hardware Information:
          MacBook Air (13-inch, Mid 2012)
          MacBook Air - model: MacBookAir5,2
          1 1.8 GHz Intel Core i5 CPU: 2 cores
          4 GB RAM
Video Information:
          Intel HD Graphics 4000 - VRAM: 1024 MB
System Software:
          OS X 10.9 (13A603) - Uptime: 0 days 0:11:45
Disk Information:
          APPLE SSD SM256E disk0 : (251 GB)
                    EFI (disk0s1) <not mounted>: 209.7 MB
                    Macintosh HD (disk0s2) /: 250.14 GB (59.72 GB free)
                    Recovery HD (disk0s3) <not mounted>: 650 MB
USB Information:
FireWire Information:
Thunderbolt Information:
          Apple Inc. thunderbolt_bus
Kernel Extensions:
Problem System Launch Daemons:
Problem System Launch Agents:
          [loaded] com.paragon.NTFS.trial.plist
          [loaded] com.paragon.NTFS.upd.plist
Launch Daemons:
          [loaded] com.adobe.fpsaud.plist
          [loaded] com.adobe.SwitchBoard.plist
          [loaded] com.microsoft.office.licensing.helper.plist
          [loaded] net.sourceforge.MonolingualHelper.plist
Launch Agents:
          [not loaded] com.adobe.AAM.Updater-1.0.plist
          [loaded] com.hp.messagecenter.launcher.plist
User Launch Agents:
          [loaded] com.adobe.ARM.df0ab5bbe6f698196fcc21e3c1e66dcb758bd911f4d637272d9d8109.plist
          [loaded] com.google.keystone.agent.plist
User Login Items:
          None
3rd Party Preference Panes:
          Flash Player
          Language Aid
          MagicPrefs
          Paragon NTFS for Mac ® OS X
Internet Plug-ins:
          AdobePDFViewer.plugin
          AdobePDFViewerNPAPI.plugin
          CMBSecurity.plugin
          Default Browser.plugin
          Flash Player.plugin
          FlashPlayer-10.6.plugin
          JavaAppletPlugin.plugin
          nplastpass.plugin
          QuickTime Plugin.plugin
          SharePointBrowserPlugin.plugin
          Silverlight.plugin
User Internet Plug-ins:
          aliedit.plugin
          Google Earth Web Plug-in.plugin
          QQMail.plugin
          QQMail.plugin
          txftn.plugin
          RealPlayer Plugin.plugin
          txftn.plugin
Bad Fonts:
          None
Top Processes by CPU:
             100%          com.apple.internetaccounts
               4%          WindowServer
               4%          com.apple.WebKit.WebContent
               2%          EtreCheck
               1%          Safari
               1%          Activity Monitor
               0%          fontd
               0%          hidd
               0%          sysmond
               0%          aosnotifyd
Top Processes by Memory:
          1.62 GB            com.apple.internetaccounts
          180 MB             com.apple.IconServicesAgent
          143 MB             com.apple.WebKit.WebContent
          111 MB             Safari
          49 MB              Dock
          45 MB              WindowServer
          37 MB              mds_stores
          37 MB              Activity Monitor
          33 MB              Finder
          25 MB              com.apple.WebKit.Networking
Virtual Memory Statistics
          35 MB              Free RAM
          1.51 GB            Active RAM
          1.48 GB            Inactive RAM
          587 MB             Wired RAM
          252 MB             Page-ins
          840 KB             Page-outs

Answer 1

@Drewli77 yup that's it. When Mail opened I chose Google/Gmail and let Mail set the account up for me.
Before doing that I had noticed com.apple.internetaccounts hogging the CPU. I went into System Preferences > Internet Accounts, waited 10 minutes for the spinning ball to stop, then deleted the Google account in there. There was only one Google account in there, despite the fact that I have four Google accounts set up in Mac Mail. Anyway this one account seemed to be what was slowing down that preference pane. After deleting Accounts.plist I re-added my accounts in Mail, which added them to the Internet Accounts preference pane, but now that preference pane (and Mail) open just fine without hogging resources.
What annoys me is the fact that hitting Delete on a message sends it to Trash, which in Mavericks corresponds to Gmail's Trash, meaning it gets purged every month (regardless of the setting you choose in Mac Mail). I've been using Option-Delete to Archive it, but I wish I could just use Delete for that, since I always Archive and rarely Trash messages. I would set another folder to be used for Trash, but sadly, all of the options under Mailbox > "Use this mailbox for" are greyed out.