Re: What do you do if your amp has no standby switch?
Get that ground switch and its related "death cap" removed and get a proper 3-conductor grounded cord installed immediately. Stop screwing around with something that couple easily kill you. We went through this recently with
chopstherocker's Bandmaster head.
About the standby switch: Scott hinted at this, but here's the reason to have one (or not). Tubes need to be warmed up before the high voltage (called B+ by the amp geeks) is applied. If the filaments (heaters) are not hot, it's rough on the tubes to hit them with the B+. In amps with a tube rectifier (small amps, tweed Fenders, JTM Marshalls) the high voltage can't get to the audio tubes before they are warmed up, because the tube rectifier has to warm up, too. By the time the recto is hot, and letting the DC flow, the other tubes are ready.
By contrast, solid-state rectifiers don't need to warm up. They can supply B+ as soon as the power is turned on. Manufacturers installed standby switches to keep B+ off the tubes until they have warmed up. So, you mostly see standby switches on amps with SS rectifiers: post-tweed Fenders, JMP and later Marshalls, most 50-watt or bigger amps.
Some amps with tube rectifiers have standby switches, but it's just for convenience, it doesn't hurt the amp by not having one.
Did I mention you should get that power cord replaced?
Also, what kind of tubes are in that amp? Some small, old amps have a special tube set that lets them operate off 120 VAC with no power transformer. You thought the ground switch/death cap setup was bad? These little monstes are even worse. Post your tube types, and we can tell from that what kind of amp it is.