get a spray bottle and put a couple tablespoons of dishwashing soap in it with water. OVER inflate the boat, but not TOO much. then Spray the entire boat until you see bubbles. Consult the MFG for patching instructions.
I joined this forum just to say Put your time and money in a new dinghy. I wasted more than two separate weeks of my season last year repairing 18year old Achilles hypalon. Started on existing patches that leaked. Thought I was done. Nope, while cruising the next weakest spot became the next leak. Also spent time and money on floorboards. Shudda put the $600+ into a new dinghy and spent more time in the water. First purchase this year was new RIB.
My advice: DON'T even think about fixing an inflatable that old.
All depends on your resources and time. You probably won't get it so airtight that you could leave it all season, but it could be good for a couple weeks at a time. I have a 25 year old and a 15 year old and got them both sealed up enough to enjoy them. Use the spray and soap and check every seam for any looseness. Any that are even remotely loose you should take apart and re-glue. Not sure if yours is hypalon or PVC, but make sure you find out and use the right glue.
Brand new is nice but some folks don't always have that option.