been pondering repurposing an old computer PSU for base duties. been running things off a car battery for short term usage, and letting it charge when not in use.
Using an old computer switching power supply likely won't work. First they are electrically noisy and will kill your receiver sensitivity. Second the designs use one of the low voltage outputs for regulation, 5 VDC - 3.3 VDC - ???, while the rest float around a bit. If the regulated output isn't loaded down enough it may not even start.
We use a number of off the shelf switching power supplies where I work for some industrial controls. I have one right now in my office loaded down with a fat power resistor on the 5 VDC rail just to get the thing to turn on so I can use the other outputs for testing a project.
About using it to charge a lead acid battery may not work well, if at all, since the high voltage outputs are a "nominal" 12 VDC on the computer power supply. You need around 13.5 VDC to 13.8 VDC to charge a "12 VDC" lead acid battery. Then there is the different charge stages to keep from damaging the battery, bulk - absorption - float, which is normally done by a smart charger. There is a bit of a difference between liquid filled, gell cell and AGM lead acid types on the charge and float voltages to content with.