What security protocol are you using on the router?
You could, ever so briefly, turn off all WiFi security protocols (WPA/WEP) and open the router up. Then try to connect. If you can connect then it is an issue, probably with the router. Remember to re-enable any preferred WiFi security protocols.
Do you use DSL?
We've been using Asus DSL-N12U units in most of our recent True Online DSL installs. These units have been working perfectly.
and it is only at home, at her work it is okay
This would seem to support the contention that the issue is with your router?
problems we've run into:
Router supports up to channel 13 for WiFi, but some devices support up to channel 14. We usually do a quick scan of neighboring APs and choose a fixed channel on the router to avoid conflict, typically channels 2 or 3. Obviously this should be monitored; and adjusted. Many routers seem to default to ch. 11, and I've seen 10+ APs on ch. 11 in a single location.
Devices go in to sleep mode then try to use the same IP address they used before, which has subsequently been handed out to another device. Re-boot the device or the router or both.
When using WPA-PSK, two different encryption protocols can be used TKIP or AES, often there is a mismatch between what the device can support or is configured to support, and what the router can support or is configured to support. Newer routers have a TKIP+AES setting.
Devices store APs so it is advisable to flush out unused APs (e.g. PTT FreeWiFi@go.th ) regularly: Settings, Wireless & networks, WiFi, press/hold and Forget.
I am currently supporting a True/DSL - Asus DSL-N12U install and the user got an SGS4 the first day it was available, so what a few months, and there have been no issues. This user just uses WiFi at home, and at work, and 3G elsewhere. I think they are prohibited from using any public WiFi on phones.