Laptop continuous beeping at startup

Clarifications

Sounds like something is wrong with the keyboard or the systemboard. Try replacing the keyboard. If that doesn't work, it is probably the systemboard that needs replacing. If it is still under warranty, I would call Toshiba to have it repaired.

Keyboard Error

Any Of the Key in Your Laptop Keyboard Is Faulty

Check The Keyboard

Hardware is the obvious thing to look at first. However, there is a virus that does this, too. I saw it infect a user's W7 PC on my network. When I attempted the OS repair, the malware prevented the mouse from clicking OK and forced the cancel button instead. It prevented process kills in Task Manager and an older system restore was prevented as well. This was on the very first reboot after infection AND it locked up the PC after the user tried logging out and back in. Next day PC was working again but I've learned when malware strikes, if you can't find it, wipe it. Since I couldn't Google any solution info, I wiped and rebuilt AND made sure I added extra AV & a personal Firewall (comodo or ZA). In my experience this is a keylogger malware that's very noisy upon first infection. I am absolutely certain this was not hardware malfunction.

The keyboard assembly has it's own interface chip mounted on the board. If that fails, a replacement keyboard from the mfgr will solve the problem. If that fails, the system board would be at fault. The ribbon cable between the two, and their associated connectors also needs some investigation. This does exhibit the classic signs of a laptop that had something spilled on it.