Let us consider very briefly what are the absolute minimum requirements for a living cell.
The complexity of the simplest known living organism is mind-boggling. You need the cell wall, the energy system, a system of self-repair, a reproduction system, and means for taking in food ( what food? All food derives ultimately from chlorophyll which has no existence outside fully functioning plants. In our supposed pre-biotic earth, there was nothing to eat or breathe before chlorophyll) and processing and expelling waste, the complex genetic code, thousands of specific proteins which all depend on each other and must be perfect or they don't work at all, a means for interpreting and replicating genetic code, osmotic regulation and other indispensable homeostasis mechanisms, plus detecting and correcting errors as they occur, and much more besides. All these features must be present and fully functioning from the start, or there is no start. There are no parts of a cell that you can take away and still have a viable living cell.
First there must be a cell wall, or else the contents would drift apart and the organism would lose it's integrity and cease to exist. Antibiotics kill bacteria by breaking their cell wall, showing without doubt that the wall is indispensable. It is a barrier but not a simple one, for example during mitosis it stretches, splits into 2 and seals itself perfectly without leaking contents. This is quite a 'simple' process, but like all the other things about the cell, if it goes wrong, the cell is dead. Cell walls are not completely impermeable, they could not work if they were. Dissolved carbon dioxide and oxygen diffuse across, also there are molecular active transport systems which move chemicals across the barrier as required. These active transport mechanisms have to be exactly right.
The cell is filled with cytoplasm, a semi liquid milieu which supports everything else physically and chemically. This is maintained homeostatically by various mechanisms in the cell, for example with the right level of acid/base balance, osmotic tension and dissolved gases etc.
Intracellular structures of several kinds exist, including ribosomes, where protein synthesis takes place under the control of DNA/RNA by means of specific protein building enzymes. The process is powered by ADP/ATP energy systems which burn carbohydrate to produce energy, just the right amount, just the right place, just the right time. Chemicals are transported across the cell to be taken to the right place at the right time for various reactions to take place.
In the middle of the cell is the nucleus which contains the massive DNA molecules, which are normally wound up on special spindles. They unravel when required and are copied on to RNA molecules. This unravelling, and re-ravelling, don't just happen, specific molecular engines exist which wrap and unwrap them just as required. This is just an outline sketch of the complexity, there is far more which is quite easily searchable but beyond the scope of this little site.
Enzymes are necessary for protein synthesis, energy production and all kinds of processes. They are themselves complicated proteins. They are necessary to make and maintain DNA, and are themselves made using precise instructions from DNA. DNA itself goes wrong sometimes, not very often considering how active it is, but often enough. Errors accumulating in DNA if not corrected would corrupt the information and eventually kill the organism but there is an automatic spell check and repair mechanism which detects errors in the nucleotide sequence and mends or cuts out and replaces them. Without this system (which incidentally is an impassable barrier to any possible beneficial mutations as it recognises and deletes random changes in the DNA, removing evolution's only possible progress mechanism) DNA would quickly accumulate errors and cease functioning, causing sickness and death as in the terrble genetic disease Xeroderma Pigmentosum.
DNA check and repair is found in all living things.
It had to be present from the beginning, or life as we know it would have been impossible.