Can one really 'lose' old bad grades and get a fresh start?

That's not necessarily the impediment you may think. The institution where I taught would not accept nor transfer credit over ten years old. Pick one or two colleges you might attend, visit their admissions offices, and ask. There's a good chance you can start fresh.

There are two things to keep in mind. Your transcript from your old institution will still be there, and you will be asked for it when you apply for any degree program. It may lessen your chances of admission, but probably not because fifteen years is a long time.

The other is that you should be honest about your education history on your resume. Once again, fifteen years is a long time. Do well now and no employer will even consider that ancient history.

Go for it!

Where I teach, not only would the age of the old courses lead to transfer problems, but our school also has the idea of academic bankruptcy, where newer courses (with some restrictions, almost none would apply to you) can be semi-erased. They remain on the transcript, but are not counted as part of the GPA. So I would say go for it, and as part of the application process check with the appropriate people there to see (a) if those old courses will be considered at all, and (b) if so, whether they have any equivalent of our academic bankruptcy.

My own undergrad history was fairly lackluster, to be honest. (Without comparing grades, I don't know how it relates to "abysmal", but that's not the point.) When I was thinking about getting a graduate degree, I started by taking classes without being formally part of the degree. (In fact, I did that for both grad programs, now that I think about it.) The nice thing about this is that they'll often let just about anyone sign up. Maybe you need to talk to a professor first and have them champion you a little, but it certainly isn't anything like as complicated as applying for a degree. Most universities are happy to have someone paying the bills for a class. (So, there is that expense, and the extra time.)

Once you have taken a course or two at the university you are interested in, you have a transcript there. Assuming you do well, you can now use that as part of your application process. If you strike up a relationship with the professor(s) of the course(s), you might actually have someone to use as a reference. If you have evidence that you are now a better caliber student than you were as a ~20 year old kid, that also gives you something to talk about to the admissions interviewers.

So, even though you may not be able to expunge old grades, you would have a pathway to start fresh at a school where your old grades won't be part of the transcript.