Ya think it could have burnt something out in the Starter relay ?
The alternator was working hard all the time I bet.
The above won't cause the problem
If you have NOTHING and you just changed the battery, that's where I'd start.
Start with the BASICS
Take a test lamp or meter, and hook to the battery block. Turn on the headlight switch, turn the key to run and turn on the heater blower. THESE WILL CAUSE A LOAD which will help you find the problem
Hook the hot lead of the lamp / meter to the hot cable clamp. It should light. If not, you have a battery/ cable problem
If not, probe to the battery hot post. If not, you have a battery or GROUND cable problem
Hook the test lamp DIRECTLY to the two battery posts. It should light. If not, you have a battery problem
Hook the test lamp back to the engine block, hook the hot lead DIRECTLY to the battery NEGATIVE post. If it lights, you have a bad ground cable.
BACK TO START
Hook the lamp to block, probe to hot battery cable clamp at battery. If it lights, so far, so good.
Move the probe to the hot cable eyelet end, wherever it goes (starter?) It should light. If not, you have a cable / connection problem
Move up to the big stud on the starter relay. Lamp should light. If so, you probably have lost the fuse link and or the main feed through the bulkhead.