I was looking for some information on HC-F2700L, I came across this page. Although I have been reading through the eevblog forums for several years, this will be the first time I write.
I recently got one of these freq counters. When I plugged in, I noticed exactly the same symptoms as mentioned in this thread. I know this thread is a bit dated but F2700L seems to be the same. I was going to open the case by taking out four screws on the back frame, I noticed that AC input is for 220V +/-10%. I am in US, here the power is 120V. Luckily, I have a 120V/240V transformer. When I plugged it to that, viola everything worked perfectly.
Not knowing if the units that folks in this thread had also required 220V, I wanted to put my comments that it looks this is a good unit. I went ahead and opened the case to look what I could do. Out of pure luck, I found a similar sized 120V transformer in my scrap box. It has about the same output voltage also. Replacing the transformer was not difficult at all. Now, the counter is operating with 120Vac in. It's very stable but like all crystal oscillators, it will drift I am sure. So, I would think installing a better 13MHz reference is a necessity.
Just to let everyone know.