I have several of the Silver Series 4.5 hp 2-cycle mowers in the self-propelled version. They are workhorses, most parts still available for repair, and they are strong, and simple to fix. They aren't as sexy as the "F" engine models, but they run just as well. There are plenty of them out there, as Lowes sold them for quite a few years. Easy to find junkers for parts machines. Incidentally, if you need to replace the self-propel drive belt, it takes a 3/8" x 33". Available at Napa stores and other larger auto parts stores for under $9. Don't pay the $22 some hardware stores charge for a belt.
Yes, if you can get it to start by priming it, yet it will not stay running, the carb jet is probably partially clogged. You have to remove the float bowl cover, and remove the screen from the middle, and the jet is below that and you can take a flat-blade screw driver and unscrew it, and remove it and you can see there are several holes that have to be cleaned for it to work properly. DO NOT forget to replace the screen, or you risk a bit of dirt being sucked up and clogging the jet again. These late-model 2-cycle plastic carbs have fixed jets, no adjustment, and they have to be CLEAN to deliver adequate fuel, as they were jetted lean to begin with. The 4.5 hp model does not have the "surging" issues the carb on the 6.5 hp models do. If you are cleaning the rest of the carb with carb cleaner, first remove the float and set it aside, as the carb cleaner will dissolve the lacquer on the cork float, and it eventually won't "float" anymore. Just set it aside, then blast away on everything else. Make sure the carb cleaner has evaporated before re-installing the float.