Alarm Clock PC?

I would expect that a timer could be used to boot the PC, Sorry no real answer on that though.
As to login, you can use the Tweak UI program. Just search for TWEAK UI from google.com to find it.
As for automatically opening a web page on bootup, set an icon for IE in the startup menu and set the home page to where you want it to go. This can be done (in IE) by selecting tools -- Internet Options. In the "general" tab add your home page to the website you want it to open to.

You didn't mention the OS. If you have XP, you can use Advanced settings to wake up the scheduler ato run your program.
control Panel-Scehduled Tasks-Add Scheduled Task-Put a check Mark in: "Open Advanced Properties for this Task When I click Finish", then click on the Schedule Tab, Then the Setings button, and put a check in the bottom box "Wake the Computer to Run This Task"

To put ON the computer automatically at a set time, there must be a feature in the BIOS for switching ON

Such a feature was seen in the SIEMENS NIXDORF Computers. and a software was also available with that pc to switch on & off the computer at a scheduled time.

The software were DESK ON & DESK OFF

There are many software available to switch off but to switch on you will have to modify your switch to a timer.
An electronic timer which make the two contacts short for 1sec at a scheduled time can be used in parallel with your computer switch.
So you can set the time in the timer to switch on.
and SWITCH OFF software is easily available at www.yasoft.km.ru

And to load ur I-net site automatically u can define it in the startup.