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It's an ambitious project for a first go, but something we can help you sort out.
The original project I think is from Silicon Chip Magazine, Dual Tracking Power Supply, June&July 2010. I don't have access to it, it's behind their paywall. I found
this schematic and repost it here. Is it what you have?
Repairing/troubleshooting electronics, the first thing you do is use your eyes. Look around for poor soldering, wiring mistakes, missing parts, burnt parts etc.
Because you are having problems with the -ve output, I would look there first. Is the transformer secondary is connected right (not mixed up center tap), jumper LK1 is out, rectifier diodes D1-D4 are in right and test OK. NO electrolytic capacitors or IC's in backwards

Double check the resistors are the right value (you can use a multimeter if the colour codes are hard to read). In-circuit some places you cannot read a resistor's value due to nearby connected parts, and one leg needs to be lifted up.
Second thing when repairing/troubleshooting electronics, is to check the power supply (internal) voltages are present and OK. Do you have the + and - 15V rails up from REG3 and REG4. The + and - 1.3VDC rails are working? The panel meter is a separate issue I would leave until later unless it's wired wrong and shorting the -V output ore something.
If you are worried about taking measurements while it's powered up, you can put black electrician's tape over the exposed mains connections. An isolation transformer is ideal but you might not have one. I go in just extra careful, that I am not touching grounded metal, use one hand, or cover the mains connections with a piece of wood or something so it's not so scary. I connect my multimeter (-) to the output common and then just move one probe and poke around, it's easier than two hands and two probes. Write down what you get for readings.
I'm not sure what Altronics
K3218 gives for assembly instructions etc. or it's just the PC boards. There was an errata, not sure if it's fixed for your build.
Errata Dual Tracking Power Supply, June-July 2010:
(1) The labels for V± and Ilim were swapped on the front panel artwork. Updated front panel artwork has been provided to the kit suppliers and is now available on the SILICON CHIP website. In addition, some constructors have found that VR7 has insufficient range to properly trim the V± reading. In this case, increase the value of its 68 ohms shunt resistor or remove the shunt resistor entirely. (08/10)
(2) There are two errors in the circuit diagram of Fig.2 in the June issue. The 820 ohms resistor connected to pin 1 of IC4a should be 68 ohms while the 100k resistor from Vout- to the top of VR7 should be 10k. The layout diagram (Fig.8) in the July 2010 issue is correct. In addition, the wiring diagram (Fig.11) shows the top and bottom connections to the VOLT ADJ header (CON6) transposed. Also, the leads to pins 5 & 6 on the panel meter must be transposed for the Altronics display. (09/10)
(3) Under some conditions, if the supply is switched off then on again soon after, the negative output current sense display may not operate correctly. To solve this, a 1N4148 or 1N4004 diode can be soldered between the output of IC2a and ground, with the anode to ground. This can either be soldered to the underside of the main PC board or to the electrically connected pads on the rear of the front panel board. (01/11)
(4) The circuit diagram on pages 70-71 of the June 2010 issue shows the wiper of VR2 connected to one end of the track when it should not be. The circuit board and overlays are correct. In addition, the two wires from the “LED PWR” connector on the main board to the front panel board should be swapped on the wiring diagram on page 84, July 2010.
Finally, the wiring for the Jaycar LED panel meter shown is correct according to the manufacturer’s data sheet but we have found that the connections to its pin 7 & 8 (or pins 5 & 6 on the front panel board) must be swapped for it to work correctly. In practice, this simply involves swapping the yellow and red wires to the display connector. (08/11)"