No crystal loading capacitors are needed. The chip was designed to work without them to minimize component count and keep manufacturing costs down.

Years ago, I did something like this to pull a prank on my son. I used X-10 dimmer modules and a CP290 controller. Every Friday night at 11PM certain lights in the house would dim, brighten, flash on and off...

He eventually found the modules and figured it out but it was a good prank while it lasted.

3.579545 Mhz  is actually the correct crystal, known commonly as a "color burst" crystal. It is often abbreviated by some suppliers as just 3.57 or 3.58 MHz.

The datasheet for the MT8870 actually specifies 3.579545 Mhz
http://www.natalnet.br/~aroca/afron/mt8870.pdf

I was using a 8ohm 0.5W speaker.One wire to ground and one PB3

And that's far too low of an impedance for an ATTiny's output pin. The speaker is trying to draw several hundred milliAmps from a pin that's not designed to supply that much current.

You need a resistor in series with with the speaker. I'd recommend around a 1K.

If you're lucky, you haven't dameged the chip.

Why don't you just replicate one?

As a good friend of mine is fond of saying, "Electronics is a bad investment, it always goes down in price."

This appears to be a single sided UNO board:

http://arduino.cc/forum/index.php?topic=65484.0

Project repository here:

https://bitbucket.org/edartuz/ul_arduino_uno/downloads

There are many single sided designs out there, I entered "Arduino single sided" into Google and looked under Images and found these right away:

http://www.theparsley.com/arduino/diy/
http://www.vonkonow.com/wordpress/2012/10/nanino-the-diy-friendly-arduino/
http://electrotormentor.blogspot.com/2011/06/single-sided-arduino-uno-board.html
http://mytronx.com/projects/myduino-v4/

They list three different LS7366 models, each with a different price.

The "R" is a 14 pin DIP, The "R-S" is a SOIC and the "R-TS" is a TSSOP package. It's in the datasheet: http://www.lsicsi.com/pdfs/LS7366.pdf

But there's no reason why a PIC or ATTiny, properly programmed of course, shouldn't work just as well. It might even be better, since the LS7366 must be reset externally (either by a pin or by reloading the counters) while a PIC or ATTiny could automatically reset its counters and start over.

How about here:

http://catalog.2k1.co.uk/acatalog/2001__LSI_CSI_Computer_Systems_Inc_140.html

I don't know anything about the company, it's just the first one I found in a search.

Edit:
Gemini claims to have them:

http://www.geminielec.com/

An LS7366 might fit your needs. It's a 32 bit counter with SPI interface that can be set in non-quadrature mode to count up or down and provide an output on overflow/underflow. I believe one of the pins can be configured as a reset as well.

Also, low frequency crystals require significantly less power to oscilate, which is a handy thing when operating small battery-powered devices such as RTC  chips or wristwatches.

A 74C922 will probably work, if you can find one.

PS/2 keyboards (and mice) have open-collector outputs. You will need pull-up resistors to read them with a scope (or anything else).

You may find this page useful:
http://www.computer-engineering.org/ps2protocol/

Code:

int HighTempA = 0.1;
int LowTempA = 100;

Well there's your problem.

Integers don't have decimals.