Steps I and II: The purpose of this study is the following: To look at how many patients achieve undetectable HIV blood levels at Week 16. To look at the absolute change in HIV blood levels from the beginning of the study to Week 16. To look at the safety and tolerability of nelfinavir (NFV) and efavirenz (EFV) when used in combination or separately in regimens containing reverse transcriptase inhibitors (RTIs). For the 2 extension studies (Weeks 49 to 144): To look at the proportion of patients whose long-term viral load remains undetectable at Week 96. To look at the time from the beginning of the study to treatment failure, with patients evaluated through Week 144. Step III: To look at the proportion of patients whose HIV blood levels are undetectable 16 weeks after starting the salvage study treatment. To assess safety, toxicity, and tolerance of salvage study drug treatment. (This study has been changed by adding new objectives.) Achieving viral suppression has been widely endorsed as the primary goal of HIV therapy. However, there are few established guidelines for devising combinations of different classes of drugs which will enhance the potential for achieving viral suppression, reducing the risk of toxicity, and preserving therapeutic options for future use. This study includes 2 anti-HIV drugs, NFV (a protease inhibitor [PI]) and EFV (a nonnucleoside reverse transcriptase inhibitor [NNRTI]), for use either alone or in combination with RTI therapy for the purpose of limiting HIV replication. Patients with treatment failure at Week 16 choose 1 of the following 3 alternative salvage therapies: 2-drug PI regimen (saquinavir and ritonavir) plus adefovir dipivoxil and L-carnitine; EFV or NFV (if not already given) plus 2 new approved anti-HIV drugs outside the study; or the best available treatment outside the study. The new RTI, adefovir dipivoxil, is added to the 2-drug PI regimen to achieve suppression of viral replication and thereby delay disease progression. (This rationale reflects a change in the treatment given to patients with treatment failure at Week 16.)