<p>I have just finished building a Tronxy P802M Prusa i3.</p>

<p>When I try to move the Z-axis, using the hardware buttons in the LCD menu (without a computer connected), it only goes down, when I both increase, and decrease, the value of Z.</p>

<p>Any suggestions?</p>

It could be a hardware fault.
First check, and compare, the control board connections to the motors of the three axes. You don't state it in your question but, presumably, the X and Y axes move correctly? If so, then compare the connections for the Z-axis motors with the connections for the motors of the axes that work as expected.
If they are correct then the problem is likely to be with the firmware.
Have you...
homed the Z-axis yet?
installed the endstops?
From
X Y Z axis only move one direction?
:
Using Marlin? Before you do a
```
G28
```
homing the axes will only move
  towards the endstops. But also check your endstops with
```
M119
```
to make
  sure they are triggered at the right time. On older Marlin, you may
  need to set
```
DISABLE_MAX_ENDSTOPS
```
(on a machine that has no max
  endstops). Newer Marlin uses
```
USE_XMIN_PLUG
```
, etc., to specifically
  set which endstops are connected. If the switches show the opposite
  state (off when triggered) then set the
```
[XYZ]_(MIN|MAX)_ENDSTOP_INVERTING
```
flags, as needed.
Likewise, from
Building a Prusa I3 3D Printer
:
You will probably also find the motor will turn only in one direction. This is normal for now as we don't have end-stops installed and haven't homed the axis - so the software doesn't know how far it can go in one direction or the other.
As Mark states in his
comment
, the P802M uses a Melzi board. From
Github: Repetier-Firmware/boards/Zonestar P802M/
:
There are some printers sold under different names like 'Zonestar
  P802M', 'Prusa i3 P802M DIY kit', 'Anet A8-B', etc, which have LCD
  20x4 with 5 keys controller connected to Melzi V2.0 board via 10 wires
  cable. Keys are connected to a single analog input using resistive
  divider.