Error when installing El Capitan: disk does not use GUID partition scheme, and I am unable to convert

Considering the comments and the results of the different listings above, Yosemite probably was installed with a hack to enable a Windows MBR only install.

I assume it was the Yosemite MBR Patch 10.10 (14A389). The patch allows you to install Yosemite to a disk with a pure MBR partition table and not the default GUID partition table with a pMBR or hybrid MBR (if Windows is installed).

Depending on the efforts needed to save your data, you may either backup everything, reinstall first Yosemite (or El Capitan) from scratch after partitioning the main disk with a GUID partition table and migrate your data from the backup and then install Windows with Boot Camp Assistant or create a GUID partition table with proper partition values manually after booting to Internet Recovery Mode. The latter will probably render Windows unbootable.

Since the first method is trivial I only describe the second one.

Add a GUID partition table manually:

This method will probably render Windows unbootable!

Preparation:

• Backup your data - especially any data on your Windows partition.
• Detach any external drive (especially your external Time Machine backup drive).

• Restart to Internet Recovery Mode by pressing alt cmd R at startup.
  The prerequisites are the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated.
  On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot to a recovery netboot image which usually is loaded from an apple/akamai server.

  I recommend ethernet because it's more reliable. If you are restricted to WIFI and the boot process fails, just restart your Mac until you succeed booting.

  Alternatively you may start from a bootable installer thumb drive (Mavericks or Yosemite) or a thumb drive containing a full system (Mavericks or Yosemite).

Adding GUID partition table and the already existing MBR partitions:

• Open Utilities -> Terminal
• Enter diskutil list to get an overview
• Unmount your main disk with diskutil umountDisk /dev/disk0 (assumimg disk0 is the disk identifier of your main disk).
• Add an GUID partition table with gpt create /dev/disk0

• Add the EFI and the existent "MBR partitions":

  The command basically looks like this:

  gpt add -b StartBlock -i IndexNumber -s NumberOfBlocks -t Type device
  

  To add all your partitions enter with the data found in your fdisk list:

  gpt add -b 40 -i 1 -s 409600 -t C12A7328-F81F-11D2-BA4B-00A0C93EC93B /dev/disk0
  gpt add -b 409640 -i 2 -s 400094952 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk0
  diskutil umountDisk /dev/disk0
  gpt add -b 400504592 -i 3 -s 1269536 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk0
  diskutil umountDisk /dev/disk0
  gpt add -b 401785650 -i 4 -s 67071375 -t EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 /dev/disk0
  

  The size of the last partition (your Windows partition) is odd because usually it's a multiple of 8. But I have no explication for this.

  The first partition is the EFI partition, the second your main Yosemite volume, the third volume is your Recovery HD and the last one is the Windows partition.

• You may label your partitions with following command if they have no names:

  gpt label -i number -l name device
  

  Example:

  gpt label -i 2 -l "Macintosh HD" /dev/disk0s2
  

• Quit Terminal by entering quit and start Disk Utility

• Check the consistency of your main volume (disk0s2)
• Reboot to your main volume and install El Capitan