Cannot Update my iPhone 6 to iOS 8.4

I have tried your advice to refresh the connection however there was no improvement in my situation. I am still seeing the the warning I posted in my OP.

I have also performed the iTunes Diagnostic Tests and my computer has passed all the tests, I have posted the results below anyone to look at.

Microsoft Windows 8 x64 Home Premium Edition (Build 9200)

ASUSTeK COMPUTER INC. X550JX

iTunes 12.2.0.145

QuickTime not available

FairPlay 2.8.28

Apple Application Support 3.2

iPod Updater Library 12.0

CD Driver 2.2.3.0

CD Driver DLL 2.1.3.1

Apple Mobile Device 8.2.1.3

Apple Mobile Device Driver 1.67.0.0

Bonjour 3.0.0.10 (333.10)

Gracenote SDK 3.06.1.3084

Gracenote MusicID 3.06.1.3084

Gracenote Submit 3.06.1.3084

Gracenote DSP 3.06.1.3084

iCloud for Windows 4.1.1.53

iTunes Serial Number 0000009AF7AA58DC

Current user is not an administrator.

The current local date and time is 2015-07-03 17:11:08.

iTunes is not running in safe mode.

WebKit accelerated compositing is enabled.

HDCP is supported.

Core Media is supported.

**** External Plug-ins Information ****

No external plug-ins installed.

Genius ID: 030a1858e7db02b865f23a6586bfc4e5

**** Network Connectivity Tests ****

Network Adapter Information

Adapter Name: {DCD42EEB-8C3F-498E-8613-8A6C95149D05}

Description: Microsoft Wi-Fi Direct Virtual Adapter #3

IP Address: 0.0.0.0

Subnet Mask: 0.0.0.0

Default Gateway: 0.0.0.0

DHCP Enabled: Yes

DHCP Server:

Lease Obtained: Thu Jan 01 08:00:00 1970

Lease Expires: Thu Jan 01 08:00:00 1970

DNS Servers:

Adapter Name: {CCD01671-1333-4392-BB6B-CDFCA8EF0A0A}

Description: Realtek 8821AE Wireless LAN 802.11ac PCI-E NIC

IP Address: 192.168.1.18

Subnet Mask: 255.255.255.0

Default Gateway: 192.168.1.1

DHCP Enabled: Yes

DHCP Server: 192.168.1.1

Lease Obtained: Fri Jul 03 17:06:12 2015

Lease Expires: Thu Jan 01 08:00:00 1970

DNS Servers: 202.156.1.16

218.186.2.16

218.186.2.6

Adapter Name: {590BFCDF-0A5B-420D-AB7D-3DD989142BAC}

Description: Realtek PCIe GBE Family Controller

IP Address: 0.0.0.0

Subnet Mask: 0.0.0.0

Default Gateway: 0.0.0.0

DHCP Enabled: Yes

DHCP Server:

Lease Obtained: Thu Jan 01 08:00:00 1970

Lease Expires: Thu Jan 01 08:00:00 1970

DNS Servers:

Active Connection: LAN Connection

Connected: Yes

Online: Yes

Using Modem: No

Using LAN: Yes

Using Proxy: No

Firewall Information

Windows Firewall is off.

Connection attempt to Apple web site was successful.

Connection attempt to browsing iTunes Store was successful.

Connection attempt to purchasing from iTunes Store was successful.

Connection attempt to iPhone activation server was successful.

Connection attempt to firmware update server was successful.

Connection attempt to Gracenote server was successful.

Last successful iTunes Store access was 2015-07-03 17:08:05.

**** CD/DVD Drive Tests ****

No drivers in LowerFilters.

UpperFilters: GEARAspiWDM (2.2.3.0),

E: HL-DT-ST DVDRAM GUC0N, Rev AS01

Drive is empty.

**** Device Connectivity Tests ****

iPodService 12.2.0.145 (x64) is currently running.

iTunesHelper 12.2.0.145 is currently running.

Apple Mobile Device Service service 3.3.0.0 is currently running.

No Universal Serial Bus Controller found.

No FireWire (IEEE 1394) Host Controller found.

Connected Device Information:

, iPhone 5s (CDMA) running firmware version 8.3

Serial Number: C39LF2XHFFGH

**** Device Sync Tests ****

Sync tests completed successfully.

I have just discovered that I cannot connect to the iTunes Update Server, I think this problem is connected to my original problem.

I have solved my problem.

If you have having difficulties downloading iOS Software:

Try resetting your router to its factory settings. This allowed my iOS software downloads to complete with no problem.

I hope this can help others.