Due largely to the recent entry of several new manufacturers into the real-time PCR (polymerase chain reaction) machinery industry, many molecular biologists
that previously could not afford such machines can now purchase these useful instruments.
(A)
that previously could not afford - wrong'that' cannot refer to molecular biologists
(B)
that once could not even afford - wrong'that' cannot refer to molecular biologists
(C)
who, prior to this entry, were unable to afford - wrong'prior to this entry' is set off using commas. Anything that is set off by commas are nonessential. But 'previously' is essential part of the sentence and also concise.
(D)
who previously could not afford - correct(E)
who at one time could not afford - wrong'one time' is not same as previously. One time refers to a point in time. Previously means 'before now'. Interchanging the terms leads to meaning change.