[Scorch]

I have a Remington Model 33 single shot 22 bolt action. It has no serial number, so I think that means it was made in the first 2 years of the 3 years of manufacture (1932 and 1933).

It could have been made any time during the production of the rifle (1932-1935). Serial numbers were not required, and Remington did not number many of their 22s as they were not considered "serious" guns.

Anybody here ever take a Mod 33 bolt apart (and put it back together successfully) and that can give me words of encouragement?

I have had Model 33s apart. There is nothing difficult or tricky about them (but I say the same thing about most guns). You most likely need a new firing pin spring, or the base of the bolt handle might be worn, or the firing pin may be peened back a bit. Start with the spring first.

I could take it to a gunsmith, but that'd cost more than I paid for the old rifle.

If you take your car to a mechanic and it costs more to repair than the car could be sold for, that says nothing about the value of the car. If you take your rifle apart and cannot put it back together or fix it properly, it is essentially worthless. The value of an item is in its utility. Things that don't work have low/no utility.