Unless the old whitfields fire box is burned out or there are other serious issues, your problems can be fixed with ease and fairly cheap too.
I did a thread on this very issue a while back and posted a schematic for a stand alone controller that you can toss together in short order.
Precision timer company makes timer relays that will replace the big doller control board.
Use a simple Casablanca fan speed controller (Triac) to run the room air fan.
You will need some #14 color coded wire (hardware store item) use stranded wire.
Keep all the original safety switches and the pressure switch that came with the stove.
You can easily make a new control panel to replace the exisiting one. (Local sheet metal shop can form one up quickly from some light gauge aluminum 1/16 thick.
Be sure to install a master switch, a fuel control switch (shuts off the feed to allow for controlled shutdown)
Install a fuse holder in the panel and keep the fuse rated at the original rating that the satove used.
The Old whits have a damper control to regulate the exhaust air flow (draft)
Run the exhaust fan at line voltage and use the draft rod to set the airflow through the fire pot.
This is a Saturday afternoon job.
The folks from wood heat stoves can supply you with a downloadable copy of the service manual for the stove.
This will show you the locations of snap switches (High and low) and other items that you need to be concerned with.
A good, reeeeeeeeeeeeeeeeeaaally good cleaning of the baffles and other internal passages is in order.
Remove the exhaust fan motor, clean it well and lubricate its bearings (two rubber plugs-remove, lube and replace pugs)
Blow out the convection fan motor and the squirrel cage fan really good and resinstall.
Be really sure that you remove the last set of internal ash baffles and get that entire area well cleaned.
The timers from Precision are as follows and here is a link to their site
http://www.precisiontimer.com/
644B-G5R one shot timer to handle the start up circuit
646B-P15RO recycle timer to handle the feed motor cycling (Heat setings/fuel feed)
You also need a KPM-1M-A potentiometer to connect to the recycle timer to adjust the "Off time" or most commonly "The heat range"
Here is the link to the Schematic
https://www.hearth.com/econtent/index.php/forums/viewthread/80023/
I am using this set up on my whitfields.
Contact JIM at precision timer co (860) 399-6253
Tell him that Robyn From Oregon sent you and what you are doing.
These very timers were what most stove makers used back a few years ago.
These things are tough and rugged and most important SIMPLE AND not too costly.
My invoice for the 3 items was $108.22 to my door
The wire needed is cheap as is the rest of the needed items.
Unless you really have some big $$$$$$$$$$ to spend, dont give up on the old Whit, just give her a control "transplant" and she will give you many many more years of great service.
The boards on these older whits had some issues and were prone to doing what you are talking about.
If yours has the touch controls they are even more touchy.
One more thing
The "latch out relay" shown in the schematic is not an absolute item but a good one.
This will stop the stove from coming back on after a power outage.
You need to press the Master reset button (Not shown)
To get one of these, just ask Jim to send you a 644 one shot timer (120V 10 amp) with external conections for a pot.
You simply leave the spades that are for the time function OPEN and the timer will stay on indefinately, but will drop out when the power is lost. (stove unplugged or power outage)
The use of the L1 (hot) and the N (Neutral) Buss bars makes wiring simple and keeps things organized.
Green is always ground
White is always neutral
Colored is always a 120V line
Use the colors as shown to keep it simple and allow following the schematic.
This stuff is all "Off the shelf" technology thats available readily.
Once you have your refit up and flying, having a spare set of timers is a great idea.
You can spec out the one shot timer that I mentioned with the external pot and then be able to use it in place of the start up timer or the latch out.
The one shot timer I used has the time set pot on the timer itself and I set it at 20 minutes.
This allows power to flow to the main timer until the low side switch snaps in and provides power to the main control timer.
You can make a simple little aluminum bracket to fasten the timers too and place it inside the stoves cabinet and close to the panel.
The only adjustments that need to be on the panel is the pot to control the recycle timers OFF time, which is the burn rate function.
Set the "On time" pot to about 1.5 to 2 seconds. This is the feed motor on time (amount it feed during any one cycle)
This adjustement is best ordered on the timer so as to keep little fingers off of it.
Mount your Triac (fan speed controller) in the panel too and your set.
Hope this helps
Snowy