Just wanted to post I did everything under the sun to try and solve this problem and got it to finally work in my situation. Wanted to post my findings.
Setup:
Dell Precision M6400 Clean install of Windows 7 Pro.
After a clean install (installed a SSD) and Windows update installed the update agent to 7.6.7600.320 windows update would get stuck at "checking for updates" and would never do anything else.
How I solved it:
I am not sure what exactly solved it. However, this is the combined methods that ended up fixing it for me.
1. Performed all 3 options on first page of this forum (trying windows update between each one and problem persisted).
2. Installed Intel Rapid Storage Technology v9.6.0.1014 from Dell.
3. Installed this update manually
https://support.microsoft.com/en-us/kb/3083324.
4. Installed this update manually
https://support.microsoft.com/en-us/kb/3102810.
5. Attempted step 1 again and then tried windows update with same problem.
6. Noticed there were a couple devices in device manager without drivers so installed those from the Dell website which consisted of multimedia card slot, graphics card(wasn't missing but was using standard vga), wifi card(wasn't missing but updated it anyways) and security control point. I think I also updated the chipset driver which fixed a couple missing devices in device manager.
7. Performed step 1 again and attempted windows update and BAM
windows found updates and installed. Windows update now works.
Why did this problem happen from a clean install? My assumption was that windows update was hanging on trying to locate driver(s) for the missing device(s) in device manager and was "hanging" on one or more of those missing devices.
Good luck!
UPDATE: 2-22-2016
Confirmed with another Dell machine. I did the following to get windows updates to work.
1. Perform step 3 above. Reboot when prompted.
2. Perform step 4 above. Open up windows updates and it should work.
Good luck!