Question : Problem: Laptop can see wireless home hotspot but cannot connect to it.

Problem: one laptop not being able to connect to  internet while the other can.
Often, a simple power restart of the wireless router fixes the issue.

Setup: 2 vista laptops sharing internet connection through a netgear wgr614 wireless router(latest firmware) connected to draytek modem.

Network connections: When one laptop does not work the wireless network adapter status is fixed on adapter is "trying to authenticate to network"  

Please help guys....

Answer : Problem: Laptop can see wireless home hotspot but cannot connect to it.

What is your wireless setup?  WPA-PSK?  WEP?

Have you tried setting the Access Point to factory defaults and leaving the Wireless Open and verify connectivity for both PC's?  If it's "trying to authenticate" that usually means the password it's sending is incorrect.  

Again, change the Wi-fi to open and verify connection from both PC's, then re-setup security.