I bought a 500 GB Seagate SATA drive (finally I could afford it) and installed
8.10 on it (on the entire drive). It is working OK
Lately, at startup, before Ubuntu boots up there is a message from the BIOS
that "S.M.A.R.T status bad, backup and replace". Then "Press F1 to resume". Is
the engine faulty in the hard disk ? There are some crackling sounds sometimes.
Is there any program for Ubuntu that diagnoses faulty hardware components ?

S.M.A.R.T is a diagnostic utility. Check this article out:
http://en.wikipedia.org/wiki/Self-Monitoring,_Analysis,_and_Reporting_Technology

I would keep the receipt for you hard drive. I have seen about ten or twenty
"new" HDDs fail so if this is what is happening with yours, I would prepare with
the appropriate backup of important files.

Yes I even had one delivered DOA. Most companies will
replace them just check the website for RMA instructions.
Crackling sounds are not good at all- its only a matter of time.
Western Digital and Seagate are both very good about replacing bad
HD's no need for receipts, they keep records by the serial numbers.
One of mine was 2 yrs old and purchased in another state I don't even
remember where, but Seagate replaced it no questions asked, since it
was still in warranty.

Did you go into the BIOS to check if you SATA drive is set OK.

From Seagate, but not specifically for Ubuntu: You can download "SeaTools" from
Seagate's web site. Nice set of diagnostics and tools. I run the
nondestructive tests once in a while, just as a health check.

You can download a .iso file and burn it to make a bootable CD. Or download the
.exe to make a bootable diskette, but you'll need a Windows PC for that.