I have faced the same issue with my HP laptop and Vista OS. I was trying to get any help from different website and also spoke with HP technical support team online. No one can help me a bit and from all where I hard different comments like; I need to Format my system or my Lan card is bad so I only need to change my Mother board and it is the only solution, this ward was came from HP Service Center in my city, and the other ward Formatting was came from HP online support team. By finally I came out with the solution. please read below:
1) Go to recovery manager.
2) Click on Advance.
3) Select Driver
4) choose Your Lan card driver and WLAN driver.(Note you cannot select more than one at a time so do it twice step by step).
5) After doing these two step open recovery manager again and select Advance.
6) Select Software re-installation.
6) Select Norton Anti virus to re-install and repair. You will be prompt with some alert massages or commands just do as it instructed.
7) It will ask you to restart your system like previous recovery steps.
And after it restart your system, you will find that your General Failure Ping issue will be resolve as it was practically tested my myself. Please let me know if it Helps any body.