In the beginning I got a click until the starter blew one of the fuses labeled IGN, then nothing. I don't know the exact failure mode but I'm assuming a short considering how fast it killed the battery without turning the starter/engine over along with the fact that it also blew a 40A fuse. If you have a click and no starter turning the engine over then it is most likely the starter. The starter draws power from a large separate feed so it sounds like the solenoid is doing it's job.
The starter isn't too bad to change but it is somewhat pricey compared to other starters I've bought over the years. It's a small and lightweight unit surprisingly for a V8, but it works.
You're in luck if you have an Advance Auto nearby, that's where I bought mine conincidentally. I was just on the site today and they have a 20% off coupon on orders over $100 (the Remy starter is $192 new not a rebuilt unit), and a $50 coupon off your next $100 order. They do this quite frequently so I end up getting most of my parts there. It helps since I maintain 5 vehicles and wind up with the $50 coupons about once a month.
The starter box was labeled, 'Toughone' but the folks in the store showed me the Delco/Remy stamped into the housing so I'm fairly confident it is in fact a Delco unit since it's new and not a rebuild. With things like starters and alternators which can easily leave you stranded I only buy OEM. As a poor kid starting out I've changed out too many lifetime warranty store brand parts year after year to realize going cheap costs more in the end with towing bills, lost time from work, and my labor of doing the same job over and over.