If you have an old passport that isn't machine readable then you need a visa.
However the chances of you actually having such a passport are virtually zero. The UK hasn't issued such passports for years and they should all have expired. Those few that may still exist would have been issued at an overseas Embassy, not at a passport office here.
I suspect you are confusing machine readability with biometrics. They are very different.
I'd be a bit doubtful of you getting a visa should you apply for one given that it was a drugs offence. The offence is not spent under US law - it never will be.
The chances of them knowing about it (unless you tell them) are low to non-existent.