The following is a brief record, based on practical experience, of what kinds of things go wrong with the ZX81 and TS1000 computers and how to go about recognizing and fixing them.
Your first clue as to what’s wrong is indicated by what does or does not come up on the screen. If nothing comes up on the TV screen, after checking to see that the TV and computer have the same channel selected, suspect a bad power adapter. Another possibility is the RF modulator (the shiny box inside the computer), but I have yet to see one of these fail.
To take the computer apart (you have to do this if you want to fix it) remove the 3 to 5 screws from the bottom (two of them are under rubber feet) and separate the top and bottom halves. The top half will have the computer printed circuit board attached. The first thing to check is the shiny grounding strip on the bottom of the circuit board. Sometimes one end (the end near the edge connection) breaks away from the circuit board. If SO, reposition it and resolder it to the board.
In nearly all repairs you will have access the top side of the circuit board by taking the screws (usually 3) from the bottom of the circuit board. After these screws are out, slowly Separate the case top from the circuit board being careful not to damage the keyboard ribbon connections. At this point you have two choices on how to proceed. !f you pull the two keyboard ribbon connections from their connectors, you risk (1) tearing them or (2) not being able to reinsert them properly with out damaging them. As you see, the risk is either damaging the connections or damaging the connections. One alternative is to set the board and case top on their edges leaving a small space between them to get at the components on the board. However, you also risk damaging the ribbon connections this way too. This is one reason Budget Robotics sells replacement membrane keyboards.
Now, what to fix. If the keyboard ribbon connections are damaged (they get brittle from the heat sometimes), replace the keyboard. However, a common mistake in diagnosing a computer problem is to assume that if the keyboard does not respond, the keyboard is bad. If a group of keys in one area of the keyboard or on opposite sides of the keyboard are the only ones that don’t work, it is probably a bad keyboard. However, if none of the keys work (and the connection is OK) or if-keys only fail in a shifted mode, it is probably a bad IC1 (integrated circuit chip number 1, one of the two largest chips, always socketed). In fact IC1 is the most common component to fail.
The CPU (the other large one, marked Z80 on top) is the second most susceptible to failure.
The other IC chips on the board rarely fail. These chips are the ROM (read only memory chip with the operating system inside) and the RAM (random access memory chip or chips, some machines have one, some two).
That is a corporate dump of the repair experience we have, good luck in you efforts.