Any ideas how to prevent unauthorized access, considering the failure of the above methods?
The first thing you need to do is to prevent unauthorized physical access. Generally speaking, all bets are off against any attacker who has gained physical access to a computer. You can make attacks more complicated for such an attacker, but you essentially cannot prevent them.
Take your examples. A Windows password? Easily bypassed with the correct tools, booted off secondary media, particularly if you're only interested in getting a copy of the data. BIOS password? Pfft, remove the CMOS battery for a short while or set the CMOS memory clear jumper; the specifics will depend on the motherboard, but the technique is well known. Or connect the hard disk to an alternative system and clone it to analyze the contents later. Full-disk encryption? A hardware keylogger will give an attacker access to the password, after which decryption is trivial. Some systems offer diagnostic ports such as JTAG, which can be used to monitor the system while it is running even if it doesn't have dedicated remote-management hardware (which many servers do); will you detect something installed and surreptiously connected to such a port? And on it goes.
There's a reason why server rooms for almost anything that matters at all are behind physical access controls, including heavy doors, reinforced walls, alarm and entry-access systems, and so on. And it isn't only about the monetary value of the hardware.
Once the computer is physically secured, the easiest way is often to install and use full disk encryption with a strong password or passphrase. It should be full disk because otherwise you're basically putting up a big sign post saying "the privacy of this stuff is important enough for me to protect with encryption", and you also run the risk of data remnants showing up in deleted locations on disk, swap space and temporary files that might not even get cleaned up properly after an improper shutdown.
In addition, all "normal" computer hygiene practices still apply: make sure to keep the OS up to date with regards to patches, have proper antivirus (and anti-other-malware) software installed and running, use a firewall, be careful what software you install, run software with minimal privileges, and so on.
Note that the above is essentially equally valid regardless of operating system. Some of the things may be done slightly differently depending on what OS you are using, but the principle of what needs to be done remains essentially the same.
Can the password of Linux be removed, just as a windows' password could be removed using similar bootable tools?
Of course. As long as you aren't protecting against physical access and using on-disk encryption, or using it in a manner that can easily be circumvented, it's a simple matter of mounting the file system with software that understands the on-disk format and allows you to manipulate the relevant files.