What are you using to get ur hotmail and gmail accounts? Try a different browser?
If your getting gmail and not hot mail, I would presume it's not a router issue.
What HW version is your router?
What FW version is currently loaded?
What ISP Service do you have? Cable or DSL?
What ISP Modem do you have? Stand Alone or built in router?
What ISP Modem make and model do you have?
Ensure DNS IP addresses are being filled in under Setup/Internet/Manual?
Turn off QoS options.
Turn off Advanced DNS Services if you have this option.
Turn on DNS Relay under Setup/Networking.
Setup DHCP reserved IP addresses for all devices on the router.
Ensure devices are set to auto obtain an IP address.
Set Firewall settings to Endpoint Independent for TCP and UDP.
What wireless modes are you using?
Try single mode G or mixed G and N?
What security mode are you using? WEP, WPA or WPA2? Preferred is WPA2. Auto TPIK and AES.
What wireless devices do you have connected?
Any cordless house phones?
Any other WiFi routers in the area?
Turn off all anti virus and firewall programs on PC while testing.
Turn off all devices accept for one wired PC while testing.