My iphone 4 won't turn on unless it is plugged into the wall. Also, my iphone won't let me turn on the wi-fi. And another problem is that it sometimes says "searching..." but it still works. And I already reseted the network setting and all settings.

Please help

Hello there, JP3199.
You've mentioned a few issues in your post so I will try to offer up some recommendations for troubleshooting each. In regards to the issue of not powering on unless plugged in the following Knowledge Base article offers some practical steps to try:
iPhone: Hardware troubleshooting
http://support.apple.com/kb/ts2802
Will not turn on, will not turn on unless connected to power, or unexpected power off
Verify that the Sleep/Wake button functions. If it does not function, inspect it for signs of damage. If the button is damaged or is not functioning when pressed, seek service.
Check if a Liquid Contact Indicator (LCI) is activated or there are signs of corrosion. Learn about LCIsand corrosion.
Connect the iPhone to the iPhone's USB power adapter and let it charge for at least ten minutes.
After at least 30 minutes, if:
The home screen appears: The iPhone should be working. Update to the latest version of iOS if necessary. Continue charging it until it is completely charged and you see this battery icon in the upper-right corner of the screen . Then unplug the phone from power. If it immediately turns off, seek service.
The low-battery image appears, even after the phone has charged for at least 20 minutes: See "iPhone displays the low-battery image and is unresponsive" symptom in this article.
Something other than the Home screen or Low Battery image appears, continue with this article for further troubleshooting steps.
If the iPhone did not turn on, reset it while connected to the iPhone USB power adapter.
If the display turns on, go to step 4.
If the display remains black, go to next step.
Connect the iPhone to a computer and open iTunes. If iTunes recognizes the iPhone and indicates that it is in recovery mode, attempt to restore the iPhone. If the iPhone doesn't appear in iTunes or if you have difficulties in restoring the iPhone, see this article for further assistance.
If restoring the iPhone resolved the issue, go to step 4. If restoring the iPhone did not solve the issue, seek service.
My issue is still not resolved. What do I do next?
Contact Apple Support.
In regard to being unable to turn on Wi-Fi, if you mean that the button is grayed out, then this article should prove useful:
iOS: Wi-Fi settings grayed out or dim
http://support.apple.com/kb/ts1559
Follow these steps to resolve the issue:
Restart your iOS device.
Make sure that airplane mode is off by tapping Settings > Airplane Mode.
Reset the network settings by tapping Settings > General > Reset > Reset Network Settings.
This will reset all network settings, including Bluetooth pairing records, Wi-Fi passwords, VPN, and APN settings.
Make sure that your device is using the latest software. To do so, connect your device to your computer and check for updates in iTunes.
If you still can't turn Wi-Fi on, please contact Apple for support and service options. If you can turn Wi-Fi on but are experiencing other issues with Wi-Fi, see how to resolve those Wi-Fi issues.
Lastly, this article should help with troubleshooting cellular network connection on your iOS device:
iPhone: Troubleshooting a cellular data connection
http://support.apple.com/kb/ts3780
Thanks for reaching out to Apple Support Communities.
Cheers,
Pedro.

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